1/1*3+1/3*5+1/5*7... ...1/49*51=?
答案:1 悬赏:30
解决时间 2021-02-26 21:51
- 提问者网友：醉人眸
- 2021-02-26 16:31
1/1*3+1/3*5+1/5*7... ...1/49*51=?
最佳答案
- 二级知识专家网友：你好陌生人
- 2021-02-26 17:44
1/1*3+1/3*5+1/5*7... ...1/49*51
=(1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+(1/7-1/9)/2+......+(1/47-1/49)/2+(1/49-1/51)/2
=(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+.......+1/47-1/49+1/49-1/51)/2
=(1-1/51)/2
=(50/51)/2
=25/51
=(1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+(1/7-1/9)/2+......+(1/47-1/49)/2+(1/49-1/51)/2
=(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+.......+1/47-1/49+1/49-1/51)/2
=(1-1/51)/2
=(50/51)/2
=25/51
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