lim(n→∞)∑(n,k=1)((-1)^(k-1))/k就是1-1/2+1/3-1/4...有几种解法给几种,

题目详情

lim(n→∞)∑(n,k=1)((-1)^(k-1))/k 就是1-1/2+1/3-1/4...有几种解法给几种,

▼优质解答

答案和解析

Xn=∑1/[k(K+1)(k+2)]=1/2∑(1/k-2/(k+1)+1/(k+2))
=1/2∑[(1/k-1/(k+1))-(1/(k+1)-1/(k+2))]
=1/4

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