问题描述: 设数列{Cn}满足Cn=2/(3n^2+3n),求{Cn}的前n项和Tn 1个回答 分类:数学 2014-10-28 问题解答: 我来补答 />这种题目是典型的裂项求和Cn=2/(3n^2+3n) =(2/3)*1/(n²+n) =(2/3)*1/[n(n+1)] =(2/3)*[1/n-1/(n+1)]∴ {Cn}的前n项和Tn=C1+C2+C3+.+Cn∴ Tn=(2/3)*[1-1/2+1/2-1/3+1/3-1/4+1/n-1/(n+1)] =(2/3)*[1-1/(n+1)] =(2/3)*n/(n+1) =2n/(3n+3) 展开全文阅读