1/1*2*3+1/2*3*4+1/3*4*5+……+1/16*17*18
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![1/1*2*3+1/2*3*4+1/3*4*5+……+1/16*17*18](/uploads/image/z/10683409-49-9.jpg?t=1%2F1%2A2%2A3%2B1%2F2%2A3%2A4%2B1%2F3%2A4%2A5%2B%E2%80%A6%E2%80%A6%2B1%2F16%2A17%2A18)
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1/1*2*3+1/2*3*4+1/3*4*5+……+1/16*17*18
1/1*2*3+1/2*3*4+1/3*4*5+……+1/16*17*18
1/1*2*3+1/2*3*4+1/3*4*5+……+1/16*17*18
1/n(n+1)(n+2) = n+2-(n+1)/n(n+1)(n+2) = 1/n(n+1) - 1/(n+1)(n+2)
原式=1/(1*2)-1/(2*3)+1/(2*3)-1/(3*4)+……+1/(16*17)-1/(17*18)
=1/2 - 1/306=76/153