Question

一乘二分之一加二乘三分之一加三乘四分之一……加三十九乘四十分之一

Answer 1

=1/2+(1/2-1/3)+(1/3-1/4)+……+(1/39-1/140)

=1/2+1/2-1/3+1/3-1/4+1/4……+1/38-1/39+1/39-1/40

=(1/2+1/2)+（1/3-1/3）+（1/4-1/4）+……（1/39-1/39）-1/40

=1-1/40

=39/40