1/1*2*3+1/2*3*4+1/3*4*5+.+1/98*99*100 等于几?
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![1/1*2*3+1/2*3*4+1/3*4*5+.+1/98*99*100 等于几?](/uploads/image/z/336209-41-9.jpg?t=1%2F1%2A2%2A3%2B1%2F2%2A3%2A4%2B1%2F3%2A4%2A5%2B.%2B1%2F98%2A99%2A100+%E7%AD%89%E4%BA%8E%E5%87%A0%3F)
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1/1*2*3+1/2*3*4+1/3*4*5+.+1/98*99*100 等于几?
1/1*2*3+1/2*3*4+1/3*4*5+.+1/98*99*100 等于几?
1/1*2*3+1/2*3*4+1/3*4*5+.+1/98*99*100 等于几?
原式=1/2(1/1*2-1/2*3)+1/2(1/2*3-1/3*4)+1/2(1/3*4-1/4*5)+.+1/2(1/98*99-1/99*100)
=1/2(1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+.+1/98*99-1/99*100)
=1/2(1/1*2-1/99*100)
=4949/19800