1乘2分之1加2乘3分之1加3乘4分之1加4乘5分之1加.加39乘40分之1等于?

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)+(1/4-1/5)+……+(1/39-1/40)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/39-1/40
=1 -1/40
=39/40