1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+........1/(20x21x22)=?
答案:3 悬赏:60 手机版
解决时间 2021-03-25 19:34
- 提问者网友：黑米和小志
- 2021-03-25 04:45
1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+........1/(20x21x22)=?
最佳答案
- 五星知识达人网友：十年萤火照君眠
- 2021-03-25 05:46
1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+.........1/(20*21*22)
=1/2[1/1*2-1/2*3]+1/2[1/2*3-1/3*4]+1/2[1/3*4-1/4*5]+...+1/2[1/20*21-1/21*22]
=1/2[1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+...+1/20*21-1/21*22]
=1/2[1/2-1/21*22]
=1/2*115/231
=115/462
=1/2[1/1*2-1/2*3]+1/2[1/2*3-1/3*4]+1/2[1/3*4-1/4*5]+...+1/2[1/20*21-1/21*22]
=1/2[1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+...+1/20*21-1/21*22]
=1/2[1/2-1/21*22]
=1/2*115/231
=115/462
全部回答
- 1楼网友：蕴藏春秋
- 2021-03-25 08:33
1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+.........1/(20*21*22)
=1/2[1/1*2-1/2*3]+1/2[1/2*3-1/3*4]+1/2[1/3*4-1/4*5]+...+1/2[1/20*21-1/21*22]
=1/2[1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+...+1/20*21-1/21*22]
=1/2[1/2-1/21*22]
=1/2*115/231
=115/462
祝你学习进步！ 天天快乐！ 加油！
=1/2[1/1*2-1/2*3]+1/2[1/2*3-1/3*4]+1/2[1/3*4-1/4*5]+...+1/2[1/20*21-1/21*22]
=1/2[1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+...+1/20*21-1/21*22]
=1/2[1/2-1/21*22]
=1/2*115/231
=115/462
祝你学习进步！ 天天快乐！ 加油！
- 2楼网友：猎心人
- 2021-03-25 07:05
1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+.........1/(20*21*22)
=1/2[1/1*2-1/2*3]+1/2[1/2*3-1/3*4]+1/2[1/3*4-1/4*5]+...+1/2[1/20*21-1/21*22]
=1/2[1/2-1/21*22]
=1/2*115/231
=115/462
=1/2[1/1*2-1/2*3]+1/2[1/2*3-1/3*4]+1/2[1/3*4-1/4*5]+...+1/2[1/20*21-1/21*22]
=1/2[1/2-1/21*22]
=1/2*115/231
=115/462
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