简单分析一下，答案如图所示
解：注意到n/(n+1)!=(n+1)/(n+1)!-1/(n+1)!=1/n!-1/(n+1)!这样1/2!+2/3!+3/4!+...+n/(n+1)!=1/1!-1/(n+1)!所以lim(n->无穷)(1/2!+2/3!+3/4!+.n/(n+1)!)=1
