## Calculus 8th Edition

Given: $\Sigma_{n =1}^{ \infty}\frac{1}{n+ncos^{2}n}$ $cosn \leq 1$ $ncos^{2} n \leq n$ $n+ncos^{2}n\leq n+n$ $\frac{1}{n+ncos^{2}n}\geq \frac{1}{2n}$ $\Sigma_{n =1}^{ \infty}\frac{1}{n+ncos^{2}n} \geq \frac{1}{2}\Sigma_{n =1}^{ \infty} \frac{1}{n}$ The given series greater than $\frac{1}{2}$ times the harmonic series . The harmonic series is divergent. Hence, the given series is also divergent.