级数1/n^2，n从1到无穷求和怎么做
答案:1 悬赏:70 手机版
解决时间 2021-04-29 11:22
- 提问者网友：回忆在搜索
- 2021-04-29 06:04
级数1/n^2，n从1到无穷求和怎么做
最佳答案
- 五星知识达人网友：千夜
- 2021-04-29 06:53
∑(n从1到正无穷) n(n+2)x^n
=x∑(n从1到正无穷) n(n+2)x^(n-1)
=x∑(n从1到正无穷)[(n+2)x^n]′
=x[∑(n从1到正无穷)(n+2)x^n]′
∑(n从1到正无穷)(n+2)x^n
=1/x[∑(n从1到正无穷)(n+2)x^(n+1)]
=1/x∑(n从1到正无穷)[x^(n+2)]′
=1/x[∑(n从1到正无穷)x^(n+2)]′
=1/x[x³/(1-x)]′
=x(3-2x)/(1-x)²
原式=x[x(3-2x)/(1-x)²]′
=x(3-x)/(1-x)³
=x∑(n从1到正无穷) n(n+2)x^(n-1)
=x∑(n从1到正无穷)[(n+2)x^n]′
=x[∑(n从1到正无穷)(n+2)x^n]′
∑(n从1到正无穷)(n+2)x^n
=1/x[∑(n从1到正无穷)(n+2)x^(n+1)]
=1/x∑(n从1到正无穷)[x^(n+2)]′
=1/x[∑(n从1到正无穷)x^(n+2)]′
=1/x[x³/(1-x)]′
=x(3-2x)/(1-x)²
原式=x[x(3-2x)/(1-x)²]′
=x(3-x)/(1-x)³
我要举报
如以上问答信息为低俗、色情、不良、暴力、侵权、涉及违法等信息，可以点下面链接进行举报！
大家都在看
推荐资讯