证明:1/(1+1)!+2/(2+1)!+…+n/(n+1)!=1-1/(n+1)!

问题描述:

证明:1/(1+1)!+2/(2+1)!+…+n/(n+1)!=1-1/(n+1)!

n/(n+1)!
=(n+1-1)/(n+1)!
=(n+1)/(n+1)!-1/(n+1)!
=
所以原式=1/1!-1/2!+1/2!-1/3!+……+1/n!-1/(n+1)!
=1-1/(n+1)!