Question

对 n\(n+1)!求和 注意分母是n+1的阶乘

Answer 1

由k/(k+1)!=(k+1-1)/(k+1)!=1/k!-1/(k+1)!,

所以1/2!+2/3!+3/4!+…+n/(n+1)!

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

=1-1/(n+1)!