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1/12+1/24+1/40+1/60+1/84+1/112+1/144+1/180（/是分数线）
题目详情
1/12+1/24+1/40+1/60+1/84+1/112+1/144+1/180（/是分数线）
▼优质解答
答案和解析
1/12+1/24+1/40+1/60+1/84+1/112+1/144+1/180
=1/2*(1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)
=1/2*(1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10)
=1/2*(1/2-1/10)
=1/2*2/5
=1/5
=1/2*(1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)
=1/2*(1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10)
=1/2*(1/2-1/10)
=1/2*2/5
=1/5
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