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计算1/2+1/6+1/12+……+1/462的值?咋玩?
题目详情
计算1/2 + 1/6 + 1/12+……+1/462的值?咋玩?
▼优质解答
答案和解析
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
＝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
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