若数列{an}的通项公式an=1/(n^2+3n+2),求数列的前n项和Sn

问题描述:

若数列{an}的通项公式an=1/(n^2+3n+2),求数列的前n项和Sn

∵an=1/(n²+3n+2)=1/(n+1)(n+2)=1/(n+1)-1/(n+2)
∴Sn=(1/2-1/3)+(1/3-1/4)+……+[1/(n+1)-1/(n+2)]
=1/2-1/(n+2)
=n/[2(n+2)]