1/1*2+1/2*3+1/3*4+···+1/1000*1001这道题怎么算
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1/1*2+1/2*3+1/3*4+···+1/1000*1001这道题怎么算
![1/1*2+1/2*3+1/3*4+···+1/1000*1001这道题怎么算](/uploads/image/z/15821225-17-5.jpg?t=1%2F1%2A2%2B1%2F2%2A3%2B1%2F3%2A4%2B%C2%B7%C2%B7%C2%B7%2B1%2F1000%2A1001%E8%BF%99%E9%81%93%E9%A2%98%E6%80%8E%E4%B9%88%E7%AE%97)
1/(1×2)+1/(2×3)+1/(3×4)+...+1/(1000×1001)
=1-1/2+1/2-1/3+1/3-1/4+...+1/1000-1/1001
=1-1/1001
=1000/1001
=1-1/2+1/2-1/3+1/3-1/4+...+1/1000-1/1001
=1-1/1001
=1000/1001