âk=1nk2ã®è¨ç®å¼ æ°å 1 2 , 2 2 , 3 2 , ⯠, n 2 ã®åï¼åè¨å·Î£ãåç §ï¼ â k = 1 n k 2 = 1 2 + 2 2 + 3 2 ⯠+ n 2 = n ( n + 1 ) ( 2 n + 1 ) 6 â 解説åç» âé¢é£ã®åç»ä¸è¦§ã®ãã¼ã¸ã¸ â å ¬å¼ã®å°åº ( k + 1 ) 3 â k 3 = 3 k 2 + 3 k + 1 ã«é ã« k = 1 , 2 , 3 , ⯠, n ä»£å ¥ãï¼ä¸ã®ããã«ç¸¦ã«ãããã¦å ãã㨠2 3 â 1 3 = 3 · 1 2 + 3 · 1 + 1 3 3 â 2 3 = 3 · 2 2 + 3 · 2 + 1 4 3 â 3 3 = 3 · 3 2 + 3 · 3 + 1 ⯠⯠+ ) ( n + 1 ) 3 â n 3 = 3 · n 2 + 3 · n + 1 ¯ ( n + 1 ) 3 â 1 = 3 â k
ãæ¢ãã®ãã¼ã¸ã¯è¦ã¤ããã¾ããã§ããããææ°ã§ãããURLãã確èªãã ããã URLã«èª¤ãããªãå ´åã¯ããµã¼ãã¼ã®ä¸å ·åãã¡ã³ããã³ã¹ãªã©ãåå ã¨ãªããã¨ãããã¾ããæéãç½®ãã¦å度ã¢ã¯ã»ã¹ã試ã¿ã¦ä¸ããã 5ç§å¾ã«èªåçã«ããããã¼ã¸ã¸ç§»åãã¾ããç§»åããªãå ´åã¯ãã¡ããã¯ãªãã¯ãã¦ãã ããã
(a+b)n ãå±éããã¨ãï¼ anârbr ã®ä¿æ°ã¯ nCr ã«ãªãï¼ ï¼nCr ãäºé ä¿æ°ã¨ããï¼ï¼ ããªãã¡ï¼ä¸è¬é 㯠nCranârbr ã«ãªãï¼ï¼r=0ï½nï¼ å±éå¼ãå ¨é¨æ¸ã㨠(a+b)n=nC0an+nC1anâ1b+nC2anâ2b2 + ··· + nCkanâkbk + ··· + nCnâ1abnâ1+nCnbn å±éå¼ãã·ã°ãè¨å·ãç¨ãã¦æ¸ã㨠(a+b)n= nCkanâkbk ï¼â»Î£ã«ã¤ãã¦ã¯ åå¿è åã解説, åé¡ç·´ç¿, Σã®å¤å½¢ åç §ï¼ãã ãï¼Î£è¨å·ãåãããªãã¦ãï¼ä»¥ä¸ã®è§£èª¬ã¯çè§£ã§ããï¼ï¼ ä¾ (a+b)7 ãå±éããã¨ãï¼ a5b2 ã®ä¿æ°ã¯ 7C2==21 ã«ãªãï¼ ä¸è¬é 㯠7Cra7ârbr å±éå¼ãå ¨é¨æ¸ã㨠(a+b)7=7C0a7+7C1a6b+7C2a5b2+7C3a4b3 +7C4a3b4+7C5a2b5+7C6ab6+7C7b7 =
ï¼1ï¼å¹³è¡ç§»åã®å ¬å¼ï¼ âi=1nai=âi=k+1n+kaiâk\displaystyle\sum_{i=1}^na_i=\displaystyle\sum_{i=k+1}^{n+k}a_{i-k}i=1ânâaiâ=i=k+1ân+kâaiâkâ ã·ã°ãã®ä¸ç«¯ï¼ä¸ç«¯ããããããã¨ãã«ãã使ãå ¬å¼ã§ãã æå³ãèããã°ãã©ã¡ãã a1a_1a1â ãã ana_nanâ ã¾ã§ã®åã表ãã¦ãããã¨ããã ãã§ãããã£ã¦ï¼ãããããã®å ¬å¼ãè¦ããªãã¦ãï¼ãã®ã¤ã©å¹³è¡ç§»åã®æå³ãèãã¦ï¼ä¸ç«¯ã»ä¸ç«¯ã»æ°åã®æ·»åã調æ´ããã°ããã ãã§ãããããï¼æ¯åæå³ãèããã®ã¯ããã©ããªã®ã§ï¼ ä¸ç«¯ã¨ä¸ç«¯ãåãæ¹åã«ãããã¦ï¼æ·»åãéæ¹åã«ãããã¨è¦ãããã¨ããªã¹ã¹ã¡ãã¾ãã âi=1nâ1i+âi=2ni2=âi=1nâ1i+âi=1nâ1(i+1)2=âi=1nâ1(i2+3i+1)\displaystyl
ã·ã°ãå ¬å¼ã£ã¦ãªãã ï¼ãã¦ï¼ã¾ãã·ã°ãã£ã¦ãªãã ï¼ã£ã¦ã¨ããããã®æ¹ãããã£ãããã§ãããï¼ æç§æ¸ããããã¨ãããªå ¬å¼ãï¼ ã±ã£ã¨è¦é£ãããã§ãããï¼ ã¨ï¼é«æ ¡çã®æã®åãä¾å¤ãªããããªæãã§ããï¼ ã§ãï¼å®éã®ã¨ããã·ã°ãå ¬å¼ã£ã¦å ¨ç¶é£ããããã¾ããï¼ å®ã¯ï¼ãã è¶³ãç®ãããã ãã§ãï¼ ä¾ãã°ï¼ã1+2+3+4+5ãè¨ç®ãããã£ã¦è¨ããããå°å¦çã§ãçãããã¾ãï¼ ãããã·ã°ãã使ã£ã¦æ¸ã表ãã¨ä»¥ä¸ã®ããã«ãªãã¾ãï¼ ããï¼ã·ã°ã表è¨ããã§ããã°ï¼ãã¨ã¯å ¬å¼ã«å ¥ããã ãã§è¨ç®ãå¯è½ã«ãªãã¨ããããã§ãï¼ ããã ãã ã¨ããããã¿ãããããªãã¨æãã¾ãï¼ ä¾ãã°ï¼ã1ã10000ã¾ã§å ¨é¨è¶³ãã¦!!ãã¨è¨ããããï¼æ®éã«è¨ç®ãããã¨ã¦ãããã©ãããã§ããï¼ã·ã°ãå ¬å¼ã使ãã°ä¸ç¬ã§ãï¼ ãã¡ããï¼é»åã使ã£ã¦ããã°ã£ã¦è¶³ãç®ã§è¨ç®ãããã®ã¨ã·ã°ãå ¬å¼ã使ã£ã¦æ±ããçãã¯ä¸è´ãã¾ãï¼ ãã¦ï¼åé¡
ã第5å ããã°ã©ãã®ããã®æ°å¦åå¼·ä¼ çºè¡¨è³æ (2015/11/21[sat])ã å 容ã¯çµ±è¨å¦ã®ç´ é¤ãããæ¹ã«ã¯åºæ¬çãªäºé ã§ããããã¯ãã«ã¨å ç©ã§è¦æ¹ãå¤ãã¦ã¿ãã¨ããç¹ã¨ããã¾ãçµ±è¨å¦ã«è¦ªãã¿ããªãæ¹ã«ãçè§£ãã¦ãããããããªã¾ã¨ãã«ãªã£ã¦ãããã¨ããã¨ããã«æ¬ã¹ã©ã¤ãã®ç¬èªæ§ãããã¨èãã¦ãã¾ãã®ã§ããã®è¾ºãè¯ããã°ã覧ãã ãã^^
Σ(ã·ã°ã)ã£ã¦ä½ 髿 ¡2å¹´çé ã«æ°åã¨ãã¦Î£ï¼ã·ã°ãï¼ã¨ããæ°å¼ãç¿ãã¾ãã ä¾ãã°ãï¼ããï½ã¾ã§ã®æ°åã®ç·åãæ±ããªããã¨ãã£ãå ´åãä¸è¨ã®ããæ°å¼ã«ãªãã¾ãã ãã®ãããã¯ç°¡åã«çè§£ã§ãã¾ããã ã¡ãªã¿ã«ãï¼ããï½ã¾ã§ã®æ°åã®ç·åã¯ä¸è¨ã®å ¬å¼ã§ç°¡åã«æ±ãããã¨ãåºæ¥ã¾ãã åç §ï¼ã¬ã¦ã¹ã®å°å¹´æä»£ã®é¸è©± ãã¨ãè¶³ãç®ã§ã¯ãªãæãç®ã®å ´åãÎ ï¼ãã¤ï¼ã¨ããæ°å¼ã使ãã¾ãã ã§ããæãç®ã®å ´åã¯å¯¾æ°ã«ãã¦æãç®ãè¶³ãç®ã«å¤æãããããΣï¼ã·ã°ãï¼ã«ãããã¨ãå¤ãã§ãã Σ(ã·ã°ã)ã®æå³ Î£ã®æå³ã¯ãåè¨ãã§ããè±èªã§è¨ãã°ããsumãã§ãã ããã¦ãΣã¯ãã·ã°ããã¨èªãã®ãªã·ã£æåï¼Ïã®å¤§æåï¼ã§ãè±èªã®ã¢ã«ãã¡ãããã®ãï¼³ãï¼ï½ã®å¤§æåï¼ã«ç¸å½ãã¾ãã ã§ããããé æåã¨ãã¦Î£ã使ããã¾ãã Σ(ã·ã°ã)ã®å ¥é ä¸éçã«ã¯ããã°ãã¼ã¿ãæ´»ç¨ãããã¨çµ±è¨å¦ãå¦ã¶æ©ä¼ãå¢ãã¦ãã¾ããã å¹¾
æ°å¤ãä½ããã®ä»æ¹ã§çµã¿åããããã®ãè¡åã¨å¼ã¶ã ãã ãã縦ã®é·ãã¨æ¨ªã®é·ãããåè¡ã¨åã§ããããªãã¦ã¯ãªããªãã ä¾ãã°ã ã¯è¡åã§ããã 髿 ¡ã¾ã§ã®ç¯å²ã§ã¯ãè¡åã¯3*3ã¾ã§ããæ±ããªãã£ãã ããããå®éã«ã¯è¡åã¯m*nè¡åãåå¨ãã(m.nã¯æ£ã®æ´æ°ã) å ¨ã¦ã«ããã¦åãç©ãªã©ã®æ¼ç®ãè¡ãªããã¨ãåºæ¥ãã è¡åã®åã¯åè¦ç´ ãã¨ã«åãåããã¨ã«ãã£ã¦å®ç¾©ãããã ãã®ãã¨ã¯ãè¡åã®åã坿ã§ãããçµååãæºãããã¨ãä¿è¨¼ããã 宿°åã¯ãåè¦ç´ ã«å®æ°ãæ¸ãããã¨ã«ãã£ã¦ å®ç¾©ããããã®æ¼ç®ã¯è¡åã«åä½è¡åã®å®æ°åãããããæ¼ç®ã¨ çãããã¨ã«æ³¨æãn*nè¡åã®åä½è¡åã¯ããå¾ã«å®ç¾©ããã ãããã®æä½ãå¯è½ãªãã¨ããè¡åã®ç·å½¢æ§ã¨å¼ã¶ã è¡åã®ç©ã¯ã ã§ä¸ããããããããã¯2*2,3*3ãªã©ã®è¡åã®æ¼ç®ã® æ¡å¼µã¨ãªã£ã¦ããã ãã®æ¼ç®ã¯çã ã¨æ¸ããããã¨ãããã éè¦ãªäºã¯ãè¡å
ããã§ã¯ã[1] ã«ã¡ãã£ã¨ãããã¨ãä»ãå ãã¦ããã¾ãã ã¯ãããã«ã¼ã®ãã«ã¿è¨å· δij ã®ããã«æ¸ãããè¨å· (i,j ã¯æ·»ãå) ãã¯ãããã«ã¼ã®ãã«ã¿ã¨å¼ã³ã¾ãã åºæ¬çã«ãã®ãããªæå³ä¸æãªè¨å·ãå°å ¥ããæç¾©ã¨ã¯ãã表è¨ãç°¡åã«ãªããã¨ãã«ããã¾ãããã¨ã㰠Σ ã¯å«ãããè¨å·ã®ä»£è¡¨æ ¼ã§ããããããã a1+a2+a3ã»ã»ã»ãã®ãããªè¡¨è¨ãããªãã¦ããããªãã®ã§ã表è¨ãç°¡åã«ãªã£ã¦ããã®ã§ããåãããããåããããããªããã¨ã¯é¢ä¿ãªããã¨ã«ãããè¦ãç®ä¸ãã£ãããããã¨ã«æç¾©ãããã¾ãã ã¨ãã«å ç©ãå¤ç©ã¨ãã£ãæ·»ãåçªå· (åºåºã®æ¹å) ãéãã° 0 ã«ãªããããªæ¼ç®ãå¤ããã¯ãã«è§£æã§ã¯ããã®ãããªãããã¨ãã¯1ã«ãªã(i.e. å¤ã¯ãã®ã¾ã¾)ãããã§ãªããã°å¤ã¯ 0 ã«ãªããè¨å·ã¯ãã°ãã°å½¹ã«ç«ã¡ã¾ãã ä»ã¾ã§ã®è¨äºã§ã¯ä¸æ¬¡å 空éã®åºåºã¯ i, j, k ã§è¡¨è¨ãã¦ãã¾ã
% $1$ ãã $n$ ã¾ã§ã®èªç¶æ° $\{1,2,3,\ldots,n\}$ ã ä¸¦ã¹æ¿ã㦠$(i,j,\ldots ,k)$ ã¨è¡¨ãããã®ã, \ommindex{é å}{ãã ããã¤}ã¨ããã ã¨ãã« $(1,2,\ldots ,n)$ ã \ommindex{èªç¶ãªé å}{ããããªãã ããã¤}ã¨ããã é å $\sigma=(i,j,\ldots ,k)$ ã®ãã¡ã® 2ã¤ã®æ°ãä¸¦ã¹æ¿ããæä½ã\ommindex{äºæ}{ããã}ã¨ããã é å $\sigma$ ã¯ä½åãã®äºæãç¹°ãè¿ã㦠èªç¶ãªé åã«ãããã¨ãã§ããã ãã®ã¨ãã«å¿ è¦ãªäºæã®åæ°ã $k$ ã¨ããã¨ã, $(-1)^k$ ã\ommindex{é åã®ç¬¦å·}{ãã ããã¤ã®ãµãã}ã¨ãã, $\sgn{\sigma}$ ã¨è¡¨ãã % $\sigma=(i,j,\ldots n)$ ã $\{1,2,3,\ldots,
<body lang=JA style='tab-interval:42.0pt'> <div class=Section1> <p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p> </div> </body> </BODY>
§ï¼ãæ°ãå ï¼ ãããããªæ°å(2) åã®ç« ã§ï¼ ã¨ãªããã¨ãå¦ç¿ãã¾ãããããã§ï¼æ°ããè¨å· Σ ãå°å ¥ãã¾ããã㮠Σ ã¯ï¼ã®ãªã·ã£æåã®å¤§æåã§ ã·ã°ã ã¨å¼ã³ï¼ï½¢ãã®è¨å·ã®å¾ãã«æ¸ãããæåãæ°å¤ãï¼k ã®å¤ãå¤å(k=1,2,3,â¦â¦,n-1,n)ããªããå ãã使¥ï½£ãæå³ãã¾ããããªãã¡ï¼ (1) ãã ã¯ï¼ï½¢k ã 1 ãã n ã¾ã§å¤å(k=1,2,3,â¦â¦,n-1,n)ããï¼a1,a2,a3,â¦â¦,an-1,an ãå ãåããã¦ãããªããï½£ã¨ãããã¨ãæå³ãã¾ãããªãï¼å¤åããã夿° k 㯠i, j ãªã©ï¼ã©ã®ãããªæåãå©ç¨ãã¦ããã¾ãã¾ããããã®è¨å·ãç¨ãã¦ï¼æåã«ç¤ºãã¾ããï¼ã¤ã®å¼ã®å·¦è¾ºã表ç¾ãã¾ãã¨ï¼ ã¨ãªãã¾ãããã®ããã«ï¼ak ã®ã¨ããã«ã¯ä¸ããããæ°åã®ä¸è¬é ãè¨å ¥ãã¾ãããããã£ã¦ï¼æåã«ç¤ºãã¾ããï¼ã¤ã®å¼ã¯ï¼ ãã®ä»çµã¿ãï¼ï¼é ã ãã«ãã¼ã£ã¦ï¼è¦ã¦ã
æ°åã®ã·ã°ã$\Sigma$ã®è¨ç®ãè¦æã¨ãã¦ãã人ã¯ããªãå¤ãã§ããã·ã°ãã®è¨å·ã¯æ°åã®åã表ãè¨å·ï¼ç·åè¨å·ï¼ã§ãã æ°åã®åãæ±ããåé¡ã¯ã»ã³ã¿ã¼è©¦é¨ãã¯ãããæ¯å¹´å¤ãã®å¤§å¦ã§ãåºé¡ããã¦ãã¾ããå¤ãã®åé¨çãè¦æã¨ãã群æ°åã¯ãã®ã·ã°ãã®è¨ç®ãéµã¨ãªãã¾ãã ããã§ã¯ã·ã°ãã®å ¬å¼ã®ç´¹ä»ã«ã¨ã©ã¾ããã¨ãªãããã®å ·ä½ä¾ãè±å¯ã«åãå ¥ããªãã説æãã¦ããããã¨æãã¾ããã»ã³ã¿ã¼è©¦é¨ã§ããåããã群æ°åã«ã¤ãã¦ã解説ãã¾ãããã®è¨äºã§ã¯åé¨åå¼·ãå§ããåã«æä½éè¦ãã¦ãããããã¨ã«ã¤ãã¦è§£èª¬ãã¦ããã¾ãã ï¼ã$\Sigma$ã®æå³ $\Sigma$ ã¯ã®ãªã·ã£æåã§ã·ã°ãã¨èªã¿ã¾ããã¢ã«ãã¡ãããã§ $S$ ã«ãããæåã§ããããã¯é«æ ¡ã®æ°å¦ã§ã¯æ°åã®åã表ãè¨å·ã¨ãã¦ç¨ãããã¾ãã ä¾ãã°æ¬¡ã®ãããªçå·®æ°åã$1,\: 2,\: 3,\: 4,\: \cdots,\: 9,\: 10$
Î£å ¬å¼ã®è¨¼æ æ°åã®åã®å ¬å¼ã®å°åº}${éå·®ã®æçå¼ãå©ç¨ãã2éãã®æ¹æ³ããã. ãããã«ãã¦ã,\ éå·®ã®åã¨,\ ãã使¬¡ã®${Σ}{$å ¬å¼ãå©ç¨ãããã¨ã«ãªã. ãã®å ¬å¼ã®å°åºèªä½ãå ¥è©¦åé¡ã¨ãªãããã®ã§,\ ãã確èªãã¦ããã¦ã»ãã. $Σk²\ ã®å°åºã¨åæ§ã®çºæ³ã§,\ Σk³,\ Σkâ´,ãé ã«æ±ãã¦ããã.$ åºçºç¹ã¨ãªãå ¬å¼\ $Σk=1+2++n=12n(n+1)$\ ã¯çå·®æ°åã®åã¨ãã¦æ±ã¾ã. $[{f(x)ãn次å¼ãªãã°,\ éå·®f(x+1)-f(x)ã¯(n-1)次å¼]$ 次ã®ãããª{éå·®ã®æçå¼}ãèããã¨,\ å ¨ã¦å³è¾ºã®æ¬¡æ°ã左辺ãã1ä½ããªã. (k+1)³-k³=3k²+3k+1 (k+1)â´-kâ´=4k³+6k²+4k+1 左辺ã¯,\ {éå·®ã®å½¢}ã§ãããã¨ãå©ç¨ã,\ åãæ±ãããã¨ãã§ãã. å³è¾ºã¯,\ 夿æ¸ã¿ã®ãã使¬¡ã®Î£å ¬å¼ãé©ç¨ãã. å¾ã¯,
homeãæ°å¦ã¡ã¢ 1ããnã¾ã§ã®æ£ã®æ´æ°ã®åã¯ãï¼ã®è¨å·ã ãã ã¨ã以ä¸ã®ããã«ã»ã»ã»ãç¨ãã¦æ¸ãäºã«ãªãã ããããΣï¼ã·ã°ãï¼è¨å·ã使ãã¨ãç°¡æ½ã«æ¸ãäºãåºæ¥ããΣã¯ãã®ããã«æ¸ãäºã§ãkã1ããnã¾ã§ä¸ã¤ãã¤å¤§ããããªãããÎ£ã®æ¨ªã®å¼ã«kã®å ·ä½å¤ãä»£å ¥ãã¦è¨ç®ããï¼ããã§ã¯kã«ä»£å ¥ããã ãï¼ãè¶³ãã¦ããäºã表ãã kã«1ããnã¾ã§ãä»£å ¥ããå ¨ã¦ã®åãæ±ããè¨å·ãªã®ã§ãç·åè¨å·ã¨å¼ã°ããã ç·åè¨ç®ã®æãåºæ¬çãªå±éå ¬å¼ã¨ãã¦ã以ä¸ã®ãããªãã®ãããï¼å¾ãã®æ¹ã«1次ã¨2次証æãæ²è¼ããï¼ã ããã«ãé常ã«éè¦ãªä¸è¬çå ¬å¼ã¨ãã¦ã以ä¸ã®ä¸æ®µç®ã®äºã¤ããããããã§ãa_kãb_kã¨ããã®ã¯f(x)ãg(x)ã¨åããããªæå³ã§ãkãå«ãä½ããã®å¼aãbã示ãã¦ãããcã¯kã®å¤ã¨ã¯é¢ä¿ãªã宿°ã§ãããäºæ®µç®ã䏿®µç®ã«å ¶ã ã®ä¾ã示ãã 以ä¸ã¯è¨ç®ä¾ã§ãããå ¬å¼ã使ã£ã¦åè§£ããããæ°åã ãã«ãªã£ã
â ãΣè¨å·ã«æ £ããã(Σè¨å·ã®å¤ãExcelã§æ±ããã«ã¯) â 解説 (1)ãk ãæ°å¤ã§æ±ããã«ã¯ï¼ å³å³ã®ããã«ã»ã«A1ã«1ï¼A2ã«2ï¼ï½¥ï½¥ï½¥ï¼A10ã«10ãæ¸ãè¾¼ãã§ãã(*1)ï¼ã»ã«A11ã«é¢æ° ãæ¸ãè¾¼ã(*2)ï¼ã»ã«A11ã®å¤ãçï¼ ï¼åæ©çãªåèï¼ (*1)ãã»ã«A1ï½A10ã«ï¼1ï½10ãæ¸ãè¾¼ãã«ã¯ A1ã«ï¼ãæ¸ãè¾¼ã A1ï½A10ããã©ãã°ã«ããå転表示ã«ãã ã¡ãã¥ã¼ãããç·¨éãâããã£ã«ãâãé£ç¶ãã¼ã¿ã®ä½æãâãç¯å²ï¼åï¼ç¨®é¡ï¼å ç®ï¼å¢åå¤ï¼1ãOKã (*2)ãã»ã«A11ã« =SUM(A1:A10) ãæ¸ãè¾¼ãã«ã¯ï¼æ¬¡ã®ãã¡ããããï¼ã¤ã®ã®æä½ãè¡ãã°ããï¼ï¼ã¤ã ãï¼ ã»ã«A11ããã¤ã³ããï¼ã·ã§ã¼ãã«ããã¢ã¤ã³ã³ã®Î£ãã¯ãªãã¯ããï¼ï¼ãã®åé¡ã®ããã«é£ç¶ãã¼ã¿ã«ç¶ãã»ã«ã§Î£ãã¯ãªãã¯ããã¨ï¼èªåçã«é£æ¥ããæ°å¤ãã¼ã¿ã®ç¯å²å ¨ä½ãå ãããã¨ãå¤ããï¼æ±ãããã®ã¨ç°ãª
âãåã表ããè¨å·Î£ã§ã¯ï¼æ¬¡ã®ããã«ãå¼ãã®å½¢ã®ã¨ããã®ã夿°ã§æå®ããããã®ãããåãã®å¤ããããçµãã®å¤ã¾ã§ãã1ãã¤å¢ããã¦ãã§ããé ã®ãåãã表ããï¼ ä¾1 k = 1+2+3+4+5ãï¼ = 15 ã«ãªãï¼ ä¾2 k = 1+2+3+4+5+6+7ãï¼ = 28 ã«ãªãï¼ ä¾3 k = 2+3+4ãï¼ = 9 ã«ãªãï¼ âãΣè¨å·ã®å é¨ã§ä½¿ãã夿°ãã¯ï¼ãå¼ãã®é¨åã¨åãæåã§ããã°ããï¼ã©ããªæåã使ããã¦ãããã¯ï¼åãæ±ããçµæã«å½±é¿ããªãï¼ï¼å¤æ°ãï¼å¼ã®é¨åã¨ç°ãªãæåã®ã¨ãã¯ï¼ç¡é¢ä¿ã«ãªããããç°¡åã«ãªã[å¾åº:ä¾6,7åç §]ï¼
ãªãªã¼ã¹ãé害æ å ±ãªã©ã®ãµã¼ãã¹ã®ãç¥ãã
ææ°ã®äººæ°ã¨ã³ããªã¼ã®é ä¿¡
å¦çãå®è¡ä¸ã§ã
j次ã®ããã¯ãã¼ã¯
kåã®ããã¯ãã¼ã¯
lãã¨ã§èªã
eã³ã¡ã³ãä¸è¦§ãéã
oãã¼ã¸ãéã
{{#tags}}- {{label}}
{{/tags}}