级数∑(n+1)^2/n!=s=

问题描述:

级数∑(n+1)^2/n!=s=
1个回答 分类:数学 2014-12-14

问题解答:

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s=∑(n+1)^2/n!=∑(n²+2n+1)/n!
=∑n²/n!+2∑n/n!+∑1/n!
=∑n/(n-1)!+2∑1/(n-1)!+∑1/n!
=∑(n-1+1)/(n-1)!+2∑1/(n-1)!+∑1/n!
=∑1/(n-2)!+3∑1/(n-1)!+∑1/n!
=e+3e+e
=5e
 
 
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