Question

1/1×3+1/3×5+1/5×7+······+1/97×99用简便方法

快快快速度啊

Answer 1

1/(1^3) + 1/(3*5) + 1/(5*7) + ...... + 1/(97*99)= (1-1/3)/2 + (1/3 - 1/5)/2 + (1/5 - 1/7)/2 + ...... + (1/97 - 1/99)/2= [(1-1/3) + (1/3 - 1/5) + (1/5 - 1/7) + ...... + (1/97 - 1/99)] / 2= [ (1 + 1/3 + 1/5 + ...... + 1/97) - (1/3 + 1/5 + `1/7 + ...... + 1/99)] / 2= [1 - 1/99] / 2= (98/99) / 2= 49/99