1|1*3+1|2*4+1|3*5+1|4*6+------+1|98*100=
答案:3 悬赏:50
解决时间 2021-10-19 10:19
- 提问者网友：我们很暧昧
- 2021-10-18 17:02
1|1*3+1|2*4+1|3*5+1|4*6+------+1|98*100=
最佳答案
- 二级知识专家网友：举杯邀酒敬孤独
- 2020-03-14 03:18
1/1*3=(1/2)(1-1/3)
1/2*4=(1/2)(1/2-1/4)
...
所以原式=(1/2)(1-1/3+1/2-1/4+1/3-1/5+...+1/98-1/100)
=(1/2)(1+1/2-1/99-1/100)
=(1/2)(3/2-199/9900)
=(1/2)(14651/9900)
=14651/19800
1/2*4=(1/2)(1/2-1/4)
...
所以原式=(1/2)(1-1/3+1/2-1/4+1/3-1/5+...+1/98-1/100)
=(1/2)(1+1/2-1/99-1/100)
=(1/2)(3/2-199/9900)
=(1/2)(14651/9900)
=14651/19800
全部回答
- 1楼网友：第四晚心情
- 2020-05-06 17:15
(1/3+1/4+1/5+1/6)*(1/4+1/5+1/6+1/7)-(1/3+1/4+1/5+1/6+1/7)*(1/4+1/5+1/6) ={(1/4+1/5+1/6)*(1/4+1/5+1/6+1/7)+1/3*(1/4+1/5+1/6+1/7)}-{(1/4+1/5+1/6+1/7)*(1/4+1/5+1/6)+1/3*(1/4+1/5+1/6)} =1/3*1/7 =1/21
- 2楼网友：独钓一江月
- 2020-10-12 23:45
1/(1*3)+1/(2*4)+...+1/(98*100)
=1/2*(1-1/3+1/2-1/4+1/3-1/5+...+1/98-1/100)
=1/2*(1+1/2-1/99-1/100)
=1/2*(9900+4950-100-99)/9900
=1/2*14651/9900
=14651/19800
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