问题描述： an=n*(n+1)*(n+2)分之一 求sn=a1+a2+a3+a4+a5+…………+an为多少?求详解. 1个回答 分类：数学 2014-11-24 问题解答： 我来补答 a‹n›=1/[n(n+1)(n+2)]=(1/2)[1/n(n+1)-1/(n+1)(n+2)]=(1/2){[1/n-1/(n+1)]-[1/(n+1)-1/(n+2)]}故S‹n›=(1/2){[(1-1/2)-(1/2-1/3)]+[(1/2-1/3)-(1/3-1/4)]+[(1/3-1/4)-(1/4-1/5)]+[(1/4-1/5)-(1/5-1/6)]+.+[(1/n-1/(n+1))-(1/(n+1)-1/(n+2))]}=(1/2){(1/2-1/6)+(1/6-1/12)+(1/12-1/20)+(1/20-1/30)+.+[1/n(n+1)-1/(n+1)(n+2)]}=(1/2)[1/2-1/(n+1)(n+2)] 展开全文阅读
