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