(Solved): Use the Ratio Test to determine w \[ \sum_{n=1}^{\infty} \frac{n}{8^{n}} \] Use the Ratio Test to ...

Use the Ratio Test to determine w \[ \sum_{n=1}^{\infty} \frac{n}{8^{n}} \] Use the Ratio Test to determine whether the series is convergent or divergent. \[ \sum_{n=1}^{\infty} \frac{(-5)^{n}}{n^{2}} \] Identify \( a_{n} \) Evaluate the following limit. \[ \lim _{n \rightarrow \infty}\left|\frac{a_{n}+1}{a_{n}}\right| \] Since \( \lim _{n \rightarrow \infty}\left|\frac{a_{n+1}}{a_{n}}\right| \) 1, Use the Ratio Test to determine whether the series is con \[ \sum_{n=1}^{\infty}(-1)^{n-1} \frac{9^{n}}{2^{n} n^{3}} \] Identify \( a_{n} \). Evaluate the following limit. \[ \lim _{n \rightarrow \infty}\left|\frac{a_{n}+1}{a_{n}}\right| \] Since \( \lim _{n \rightarrow \infty}\left|\frac{a_{n+1}}{a_{n}}\right| \longrightarrow 1 \) ?