Question

数列{an}的前n项和Sn=n^2/(3n+2),求liman的值,要具体过程,

Answer 1

an=sn-sn-1=n^2/(3n+2)-(n-1)^2/(3n-1)=(3n^2+n-2)/(9n^2+3n-2)

lim an=lim (3n^2+n-2)/(9n^2+3n-2)=lim (3n^2+n-2/3-4/3)/(9n^2+3n-2)=1/3