## Calculus 8th Edition

$\sum\frac{sin2n}{1+2^{n}}\leq \sum \frac{1}{1+2^{n}}$ $\sum\frac{1}{1+2^{n}}\lt \sum \frac{1}{2^{n}}$ Here, $\sum \frac{1}{2^{n}}$ is a geometric series with common ratio $r=1/2$. Hence, the series is convergent.