## Calculus: Early Transcendentals 8th Edition

Ratio Test: $\lim\limits_{n \to \infty}|\dfrac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\dfrac{\frac{(10)^{n+1}}{(n+2)4^{2(n+1)+1}}}{\frac{(10)^{n}}{(n+1)4^{2n+1}}}|$ $=\lim\limits_{n \to \infty}|\frac{n+1}{n+2} \cdot \frac{10}{16}|$ $=\lim\limits_{n \to \infty}|\frac{1+1/n}{1+2/n} \cdot \frac{10}{16}|$ $=\frac{5}{8} \lt 1$ The series is absolutely convergent.