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)!
