作者Honor1984 (希望愿望成真)
看板trans_math
标题Re: [级数] 三个相乘?
时间Wed Mar 26 07:37:00 2014
※ 引述《anger50322 (江)》之铭言：
: (1/1‧2‧3)+(2/2‧3‧4)+(3/3‧4‧5)+......+[1/n(n+1)(n+2)]=n(n+3)/4(n+1)(n+2)
^^ ^^
1 1
1
左式 = Σ -----------
k(k+1)(k+2)
n 1 2 1
= (1/2)Σ [--- - ---- + ----]
k=1 k k+1 k+2
= (1/2)[ 1/1 - 1/2 - 1/(n+1) + 1/(n+2)]
n(n+3)
= --------
4(n+1)(n+2)
--
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1F：推 anger50322:非常感谢!!!! 03/26 11:07
2F：→ yhliu :1/[k(k+1)(k+2)]=(1/2){1/[k(k+1)]-1/[(k+1)(k+2)]} 04/01 20:18
3F：→ yhliu :加总式相消结果=(1/2){1/(1．2)-1/[(n+1)(n+2)]} 04/01 20:19