求助,利用柯西收敛准则证明数列Xn=∑n⼀是发散的

2025-04-07 13:26:32
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回答1:

对任意epsilon>0,存在正整数N = [1/epsilon]+1,使得对任意n>N,任意正整数p,有 |x(n+p)-x(n)| = 1/(n+1)!+1/(n+2)!+…+1/(n+p)! < 1/(n+1)n+1/(n+2)(n+1)+…+1/(n+p)(n+p-1) = 1/n-1/(n+p)