1/1×3+1/2×4+1/3×5+.+1/49×51

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1/1×3+1/2×4+1/3×5+.+1/49×51
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1/1×3+1/2×4+1/3×5+.+1/49×51
1/1×3+1/2×4+1/3×5+.+1/49×51

1/1×3+1/2×4+1/3×5+.+1/49×51
1/[n*(n+2)]=1/2*[1/n-1/(n+2)]
2*原式=1/1-1/3+1/2-1/4+1/3-1/5+...+1/49-1/51=1+1/2-1/50-1/51=1862/1275
原式=931/1275

1/1×3=1-1/3
1/2×4=1/2-1/4
1/3×5=1/3-1/5
1/1×3+1/2×4+1/3×5+......+1/49×51=1+1/2-1/51=151/102