A PHP Error was encountered

Severity: Warning

Message: mkdir(): Permission denied

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/aaa9910e8dccae48a6e422cac87c143d.gif): failed to open stream: No such file or directory

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): Permission denied

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/7d6c51cf7fda42b91e4d1432088e5fbb.gif): failed to open stream: No such file or directory

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): Permission denied

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/9227c81e19660ad7baae25cb77b9545c.gif): failed to open stream: No such file or directory

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): Permission denied

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/5351ed5156c5b31e8b783d3991519033.gif): failed to open stream: No such file or directory

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): Permission denied

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/426ebf1b45328a2c49930baaa26b6a3d.gif): failed to open stream: No such file or directory

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): Permission denied

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/d57ec3ba4b0b789c5b06d0b0268421c4.gif): failed to open stream: No such file or directory

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): Permission denied

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/0aaa0aace631521faa4fbb80d1612866.gif): failed to open stream: No such file or directory

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): Permission denied

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/7aa571c094c8c00e44fa95b562d7f518.gif): failed to open stream: No such file or directory

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): Permission denied

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/2c40bad21170e964b155950116bdc93c.gif): failed to open stream: No such file or directory

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): Permission denied

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/59ccd94902fa9c2b4d2599605a5ac5d9.gif): failed to open stream: No such file or directory

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): Permission denied

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/ab5158355eda1cf98c8b78e5bf8f4000.gif): failed to open stream: No such file or directory

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): Permission denied

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/5c4eb4292f1bf7129755a9bf52023dd7.gif): failed to open stream: No such file or directory

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): Permission denied

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/3ae184b7f48066d7e3516ba1a19e03f7.gif): failed to open stream: No such file or directory

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): Permission denied

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/05bbace331044acfa646b78109a32f74.gif): failed to open stream: No such file or directory

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

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수학동아 - 폴리매스
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[수학 정보] 끄적끄적(이라기엔 2시간 투자)
황금 열쇠 2020.08.05 09:49 조회 909
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페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

 

가로줄: 식 / 세로줄: n의 범위  n<-1   n=-1   -1< n< 0   n=0   0< n<1   n=1   1<n 
\frac{n}{m}+\frac{n^{2}}{m}+\frac{n^{3}}{m}+\frac{n^{4}}{m}+...... (m\neq 0)    ?    ?       ?    0   \frac{n}{m-nm}   ∞   ∞
\frac{n}{m}-\frac{n^{2}}{m}+\frac{n^{3}}{m}-\frac{n^{4}}{m}+...... (m\neq 0)    -∞    -∞     \frac{n}{nm-m}    0      ?    ?    ?
\frac{m}{n}+\frac{m}{n^{2}}+\frac{m}{n^{3}}+\frac{m}{n^{4}}+......    ?      ?       ?    ?    ∞*m  ∞*m  \frac{m}{n-1}
\frac{m}{n}-\frac{m}{n^{2}}+\frac{m}{n^{3}}-\frac{m}{n^{4}}+......    \frac{m}{1-n}  ∞*m      ∞*m    ?      ?    ?   ?

 

 

이 4개 식이랑 표의 값으로 등식 만들어서 양변에 -1곱하면 또 다른 4개의 식 만들수 있습니다. (총 8개)

일명 "분수의 거듭제곱의 무한한 덧셈뺄셈"

 

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  •  
    리프 Lv.7 2020.08.08 04:18

    참고로 말씀드리자면 등비수열의 합 공식이 이미 존재합니다

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