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1/1*3+1/2*4+1/3*5+.1/18*20=?
题目详情
1/1*3+1/2*4+1/3*5+.1/18*20=?
▼优质解答
答案和解析
1/1×3 + 1/2×4 + 1/3×5 +...+ 1/18×20
= (1/2)×(1 - 1/3) + (1/2)×(1/2 - 1/4) +...+ (1/2)×(1/18 - 1/20)
= (1/2)×(1 - 1/3 + 1/2 - 1/4 + ...+ 1/17 - 1/19 + 1/18 - 1/20)
= (1/2)×(1 + 1/2 - 1/19 - 1/20)
= (1/2)×531/380
= 531/760
= (1/2)×(1 - 1/3) + (1/2)×(1/2 - 1/4) +...+ (1/2)×(1/18 - 1/20)
= (1/2)×(1 - 1/3 + 1/2 - 1/4 + ...+ 1/17 - 1/19 + 1/18 - 1/20)
= (1/2)×(1 + 1/2 - 1/19 - 1/20)
= (1/2)×531/380
= 531/760
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