计算1/2 + 1/6 + 1/12+……+1/462的值?咋玩?

来源:学生作业帮助网 编辑:六六作业网 时间:2024/05/15 02:49:08
计算1/2+1/6+1/12+……+1/462的值?咋玩?计算1/2+1/6+1/12+……+1/462的值?咋玩?计算1/2+1/6+1/12+……+1/462的值?咋玩?1/2+1/6+1/12+

计算1/2 + 1/6 + 1/12+……+1/462的值?咋玩?
计算1/2 + 1/6 + 1/12+……+1/462的值?咋玩?

计算1/2 + 1/6 + 1/12+……+1/462的值?咋玩?
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