用数列极限证明lim(n^2+n+1)/(2n^2+1)=1/2
问题描述：
用数列极限证明lim(n^2+n+1)/(2n^2+1)=1/2
答
对于任意ε>0
令N=max(1,3/(4ε))
当n>N时
|(n^2+n+1)/(2n^2+1)-1/2|
=|2n^2+2n+2-2n^2-1|/[2(2n^2+1)]
=(2n+1)/[2(2n^2+1)]
分子2n+12(2n^2)=4n^2