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) <1/n据柯西收敛准则，得证。
