Chapter 11 - Section 11.2 - Series - 11.2 Exercises - Page 716: 37

Diverges

$\lim _{n\rightarrow \infty }\ln \left( \dfrac {n^{2}+1}{2n^{2}+1}\right) =\lim _{n\rightarrow \infty }\ln \left( \dfrac {1+\dfrac {1}{n^{2}}}{2+\dfrac {1}{n^{2}}}\right) =\ln \dfrac {1}{2}\neq 0\Rightarrow \sum ^{\infty }_{n=1}\ln \left( \dfrac {n^{2}+1}{2n^{2}+1}\right) $ Diverges