1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+........1/(20x21x22)=?
答案:3 悬赏:20
解决时间 2021-02-01 16:43
- 提问者网友：妖精ξ也會哭
- 2021-02-01 12:04
高手说哈!!
最佳答案
- 二级知识专家网友：两不相欠
- 2021-02-01 13:20
1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+.........1/(20*21*22)
=1/2[1/畅花扳拘殖饺帮邪爆矛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/畅花扳拘殖饺帮邪爆矛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：修女的自白
- 2021-02-01 14:08
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畅花扳拘殖饺帮邪爆矛7;21*22]
=1/2[1/2-1/21*22]
=1/2*115/231
=115/462
- 2楼网友：都不是誰的誰
- 2021-02-01 13:34
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
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