1-1/2+1/3-1/4+1/5-1/6+…+1/99-1/100 1/(101+1)+1/(2+102)+1/(3+
答案:1 悬赏:60 手机版
解决时间 2021-02-15 18:11
- 提问者网友:骨子里的高雅
- 2021-02-15 02:21
1-1/2+1/3-1/4+1/5-1/6+…+1/99-1/100 1/(101+1)+1/(2+102)+1/(3+103)+…+1/(49+149)+1/(50+150)
最佳答案
- 五星知识达人网友:末日狂欢
- 2021-02-15 02:32
分子=1-1/2+1/3-1/4+1/5-1/6……+1/99-1/100
=1+1/2+1/3+1/4+1/5+1/6……+1/99+1/100-2*(1/2+1/4+1/6+......+1/100)
=1+1/2+1/3+1/4+1/5+1/6……+1/99+1/100-(1+1/2+1/3+......+1/50)
=1/51+1/52+1/53+......+1/100
分母=1/102+1/104+1/106+......+1/200
=1/2*(1/51+1/52+1/53+......+1/100)
分子除分母=1/(1/2)=2
=1+1/2+1/3+1/4+1/5+1/6……+1/99+1/100-2*(1/2+1/4+1/6+......+1/100)
=1+1/2+1/3+1/4+1/5+1/6……+1/99+1/100-(1+1/2+1/3+......+1/50)
=1/51+1/52+1/53+......+1/100
分母=1/102+1/104+1/106+......+1/200
=1/2*(1/51+1/52+1/53+......+1/100)
分子除分母=1/(1/2)=2
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