Question

Determine whether the sequence:

Answer 1

$\\ \lim_{n \to \infty} \ln{ (2n^2+1) }-\ln{(n^2+1)} \\ \\ \lim_{n \to \infty} \ln{ \frac{2n^2+1}{n^2+1} } \\ \\ \lim_{n \to \infty} \ln{ \frac{ \frac{2n^2}{n^2} + \frac{1}{n^2}}{ \frac{n^2}{n^2}+ \frac{1}{n^2}} } \\ \\ \lim_{n \to \infty} \ln{ \frac{ 2 + \frac{1}{n^2}}{ 1+ \frac{1}{n^2}} } \\ \\ \ln{ \frac{ 2 + 0}{ 1+ 0} } \\ \\ \ln{2}$