n/(n+1)!=[(n+1)-1]/(n+1)!=1/n!-1/(n+1)!
故1/2!+2/3!+3/4!+...+n/(n+1)!
=1-1/2!+1/2!-1/3!+1/3!-1/4!+.+1/n!-1/(n+1)!=1-1/(n+1)!