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已知1/2+1/5+1/8+1/11+1/20+1/41+1/110+1/1640=1,求-1/2-1/5-1/8+1/11-1/20-1/41+1/100+1/1640的值
题目详情
已知1/2+1/5+1/8+1/11+1/20+1/41+1/110+1/1640=1,求-1/2-1/5-1/8+1/11-1/20-1/41+1/100+1/1640的值
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答案和解析
1/2+1/5+1/8+1/11+1/20+1/41+1/110+1/1640=1,
所以1/11+1/110=1-(1/2+1/5+1/8+1/20+1/41+1/1640)=1-1/2-1/5-1/8-1/20-1/41-1/1640
所以-1/2-1/5-1/8-1/20-1/41-1/1640=1/11+1/110-1
所以-1/2-1/5-1/8+1/11-1/20-1/41+1/110-1/1640
=1/11+1/110-1+1/11+1/110
=2/11+1/55-1
=10/55+1/55-1
=11/55-1
=1/5-1
=-4/5
所以1/11+1/110=1-(1/2+1/5+1/8+1/20+1/41+1/1640)=1-1/2-1/5-1/8-1/20-1/41-1/1640
所以-1/2-1/5-1/8-1/20-1/41-1/1640=1/11+1/110-1
所以-1/2-1/5-1/8+1/11-1/20-1/41+1/110-1/1640
=1/11+1/110-1+1/11+1/110
=2/11+1/55-1
=10/55+1/55-1
=11/55-1
=1/5-1
=-4/5
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