问题描述: 计算1/1*2*3+1/2*3*4+1/3*4*5+...+1/98*99*100 1个回答 分类:数学 2014-10-07 问题解答: 我来补答 1/(1*2*3) = (3-2)/(1*2*3) = 1/(1*2) - 1/(2*3)同理,1/(2*3*4) = 1/(2*3) - 1/(3*4)由此类推,得1/1*2*3+1/2*3*4+1/3*4*5+...+1/98*99*100= 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/(1*2) - 1/(99*100)= 4949/9900≈ 0.4999 展开全文阅读