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(1-1/2+1/3-1/4+...+1/99-1/100)/(1/100*102+1/100*104+...+1/100*200)的简算方法
题目详情
(1-1/2+1/3-1/4+...+1/99-1/100)/(1/100*102+1/100*104+...+1/100*200)的简算方法
▼优质解答
答案和解析
(1-1/2+1/3-1/4+...+1/99-1/100)/(1/100*102+1/100*104+...+1/100*200)
=(1+1/3+..+1/99-1/2-1/4-...-1/100) / (1/100(1/102+1/104+..+1/200))
=[1+1/2+..+1/100-2(1/2+1/4+..+1/100)] /[1/200(1/51+..+1/100)]
=[1+1/2+..+1/100-(1/1+1/2+..+1/50)]÷[1/200(1/51+..+1/100)]
=(1/51+..+1/100)÷[1/200(1/51+..+1/100)]
=200
=(1+1/3+..+1/99-1/2-1/4-...-1/100) / (1/100(1/102+1/104+..+1/200))
=[1+1/2+..+1/100-2(1/2+1/4+..+1/100)] /[1/200(1/51+..+1/100)]
=[1+1/2+..+1/100-(1/1+1/2+..+1/50)]÷[1/200(1/51+..+1/100)]
=(1/51+..+1/100)÷[1/200(1/51+..+1/100)]
=200
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