1/1*2+1/2*3+1/3*4+1/4*5+……+1/199*200
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![1/1*2+1/2*3+1/3*4+1/4*5+……+1/199*200](/uploads/image/z/1131710-14-0.jpg?t=1%2F1%2A2%2B1%2F2%2A3%2B1%2F3%2A4%2B1%2F4%2A5%2B%E2%80%A6%E2%80%A6%2B1%2F199%2A200)
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1/1*2+1/2*3+1/3*4+1/4*5+……+1/199*200
1/1*2+1/2*3+1/3*4+1/4*5+……+1/199*200
1/1*2+1/2*3+1/3*4+1/4*5+……+1/199*200
1/1×2=1-1/2 1/2×3=1/2-1/3 1/3×4=1/3-1/4 ………… 1/n*(n+1)=1/n-1/(n+1) 以上各式相加得 1/1*2+1/2*3+1/3*4+1/4*5+……+1/n*(n+1) =1-1/(n+1) 所以把200带入得 199/200 查看原帖>>