级数n/(n+1)(n+2)(n+3)和是多少
答案:3 悬赏:30
解决时间 2021-01-11 08:25
- 提问者网友：轻浮
- 2021-01-10 09:13
级数n/(n+1)(n+2)(n+3)和是多少
最佳答案
- 二级知识专家网友：佘樂
- 2021-01-10 10:27
n/(n+1)(n+2)(n+3)=(n+1-1)/(n+1)(n+2)(n+3)=1/(n+2)(n+3)-1/(n+1)(n+2)(n+3)=[1/(n+2)-1/(n+3)]-(1/2)[1/(n+1)(n+2)-1/(n+2)(n+3)],求和得到1/3-(1/2)*(1/(2*3))=1/4.
全部回答
- 1楼网友：雪起风沙痕
- 2021-01-10 12:11
0.25
- 2楼网友：行雁书
- 2021-01-10 11:24
n/(n+1)(n+2)(n+3)=[3(n+1)-(n+3)]/2(n+1)(n+2)(n+3)
=3/2(n+2)(n+3)-1/2(n+2)(n+3)
所以级数和为(3/2)(1/(1+2))-(1/2)(1/(1+1))=1/4
=3/2(n+2)(n+3)-1/2(n+2)(n+3)
所以级数和为(3/2)(1/(1+2))-(1/2)(1/(1+1))=1/4
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