n/(n+1)!
=[(n+1)-1]/(n+1)!
=(n+1)/(n+1)!-1/(n+1)!
=1/n!-1/(n+1)!
所以左边=1/1!-1/2!+1/2!-1/3!+……+1/n!-1/(n+1)!
=1-1/(n+1)!