n/(n+1)!=(n+1-1)/(n+1)!=(n+1)/(n+1)!-1/(n+1)!=1/n!- 1/(n+1)!
所以 原式=1/1!-1/2!+ 1/2!-1/3!+ 1/3!-1/4!+...+ 1/n!-1/(n+1)!
=1-1/(n+1)!
n/(n+1)!=(n+1-1)/(n+1)!=(n+1)/(n+1)!-1/(n+1)!=1/n!- 1/(n+1)!
所以 原式=1/1!-1/2!+ 1/2!-1/3!+ 1/3!-1/4!+...+ 1/n!-1/(n+1)!
=1-1/(n+1)!