计算1/2 + 1/6 + 1/12+……+1/462的值?咋玩?

题目

计算1/2 + 1/6 + 1/12+……+1/462的值?咋玩?

答案

1/2 + 1/6 + 1/12+……+1/462＝1/(1*2)+1/(2*3)+1/(3*4)+...+1/(20*21)+1/(21*22)＝1/2+(1/2 - 1/3)+(1/3 - 1/4)+...+(1/20 -1/21)+(1/21 -1/22) (中间每相邻两项正负相消)=1/2 +1/2 －1/22=1－1/22＝21/22...