(1-1/2+1/3-1/4...+1/49-1/50)/{1/(1+51)+1/(2+52)+1/(3+53)+1/(4+54)+...+1/(24+74)+1/(25+75)
答案:2 悬赏:30
解决时间 2021-12-15 02:59
- 提问者网友：前事回音
- 2021-12-14 08:18
过程
最佳答案
- 二级知识专家网友：无字情书
- 2021-12-14 08:36
分子=1-1/2+1/3-1/4......+1/49-1/50
=1-1/2+1/3-1/4......+1/49-1/50+(1/2+1/4+1/6+......+1/50)-(1/2+1/4+1/6+......+1/50)
=1+1/2+1/3+1/4......+1/49+1/50-2*(1/2+1/4+1/6+......+1/50)
=(1+1/2+1/3+1/4+1/25)+1/26......+1/49+1/50-(1+1/2+1/3+......+1/25)
=1/26+......+1/49+1/50
分母=(1/52+1/54+...1/100)=1/2(1/26+......+1/49+1/50)
∴原式=分子/分母=1/（1/2）=2
=1-1/2+1/3-1/4......+1/49-1/50+(1/2+1/4+1/6+......+1/50)-(1/2+1/4+1/6+......+1/50)
=1+1/2+1/3+1/4......+1/49+1/50-2*(1/2+1/4+1/6+......+1/50)
=(1+1/2+1/3+1/4+1/25)+1/26......+1/49+1/50-(1+1/2+1/3+......+1/25)
=1/26+......+1/49+1/50
分母=(1/52+1/54+...1/100)=1/2(1/26+......+1/49+1/50)
∴原式=分子/分母=1/（1/2）=2
全部回答
- 1楼网友：寂寞的炫耀
- 2021-12-14 10:04
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