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1/3+1/5+1/7+1/9+1/11+1/15+1/35+1/45+1/231可是关键是怎样算更简便.
题目详情
1/3+1/5+1/7+1/9+1/11+1/15+1/35+1/45+1/231
可是关键是怎样算更简便.
可是关键是怎样算更简便.
▼优质解答
答案和解析
1/3+1/5+1/7+1/9+1/11+1/15+1/35+1/45+1/231
=1/3+1/5+1/7+1/9+(1/11+1/231)+（1/2）(1/3-1/5+1/5-1/7)+1/45
=1/3+1/5+1/7+1/9+2/21+(1/2)(1/3-1/7)+1/45
=1/3+1/5+1/7+1/9+1/3-1/7+1/45
=2/3+14/45+1/45
=2/3+1/3
=1.
=1/3+1/5+1/7+1/9+(1/11+1/231)+（1/2）(1/3-1/5+1/5-1/7)+1/45
=1/3+1/5+1/7+1/9+2/21+(1/2)(1/3-1/7)+1/45
=1/3+1/5+1/7+1/9+1/3-1/7+1/45
=2/3+14/45+1/45
=2/3+1/3
=1.
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