Question

1乘二分之一加二乘三分之一……三十九乘四十分之一

Answer 1

1/n-1/(n+1)=1/n*(n+1)

故：

1/(1*2)+1/(2*3)+1/(3*4)+……+1/(39*40)

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

=1-(1/2-1/2)-(1/3-1/3)-……(1/39-1/49)-1/40

=1-1/40

=39/40