谁有这道题的简便算法?

题目

谁有这道题的简便算法?
1/4+1/28+1/70+…+1/9700＝?

答案

1/4+1/28+1/70+...+1/9700 =1/(1*4)+1/(4*7)+1/(7*10)+...1/(97*100) =1/3(1/1-1/4)+1/3(1/4-1/7)+1/3(1/7-1/10)+...1/3(1/97-1/100) =1/3(1-1/4+1/4-1/7+1/7-1/10+...1/97-1/100) =1/3(1-1/100) =1/3*(99/100) =33/...