1/1+2+1/1+2+3+1/1+2+3+4+……+1/1+2+3+……+50?快
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![1/1+2+1/1+2+3+1/1+2+3+4+……+1/1+2+3+……+50?快](/uploads/image/z/13394259-27-9.jpg?t=1%2F1%2B2%2B1%2F1%2B2%2B3%2B1%2F1%2B2%2B3%2B4%2B%E2%80%A6%E2%80%A6%2B1%2F1%2B2%2B3%2B%E2%80%A6%E2%80%A6%2B50%3F%E5%BF%AB)
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1/1+2+1/1+2+3+1/1+2+3+4+……+1/1+2+3+……+50?快
1/1+2+1/1+2+3+1/1+2+3+4+……+1/1+2+3+……+50?
快
1/1+2+1/1+2+3+1/1+2+3+4+……+1/1+2+3+……+50?快
1+2+……+n=n(n+1)/2
所以1/(1+2+……+n)=2/n(n+1)=2*[1/n-1/(n+1)]
所以原式=2*(1/2-1/3+1/3-1/4+……+1/50-1/51)
=2*(1/2-1/51)
=49/51