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1/3*5+1/5*7+1/7*9+1/9*11+1/11*13=?
题目详情
1/3*5+1/5*7+1/7*9+1/9*11+1/11*13=?
▼优质解答
答案和解析
1/3*5+1/5*7+1/7*9+1/9*11+1/11*13
=1/2[(1/3-1/5)+(1/5-1/7)+.(1/11-1/13)]
=1/2(1/3-1/5+1/5-1/7+1/7-.+1/11-1/13)
=1/2(1/3-1/13)
=1/2*(10/39)
=5/39
=1/2[(1/3-1/5)+(1/5-1/7)+.(1/11-1/13)]
=1/2(1/3-1/5+1/5-1/7+1/7-.+1/11-1/13)
=1/2(1/3-1/13)
=1/2*(10/39)
=5/39
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