简算:1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+······+1/(39*40) = 急

问题描述:

简算:1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+······+1/(39*40) = 急

1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+······+1/(39*40)
=1-1/2+1/2-1/3+1/3-1/4+...+1/39-1/40
=1-1/40
=39/40