Calculus 2: Alternating series and absolute convergence

Consider the series that starts from one goes to infinity: $(-1)^n \cdot \frac{1}{n}$. Will the alternating harmonic series converge or diverge?

Consider the series which goes from 1 to infinity: $(-1)^{n+1} \cdot \frac{5n + 3}{2n - 7}$. Will this series converge or diverge?

Consider the series: $\frac{(-1)^{n+1}}{5^n}$. Will the series converge or diverge?

Consider the series $(-1)^n \cdot \frac{n}{\ln(n)}$. Will the series converge or diverge?

Let's say the series is $(-1)^{n+1} \cdot \frac{\ln(n)}{n}$. Will it converge or diverge?

Consider the series $\frac{\cos(n \pi)}{n}$. Can we apply the alternating series test to it?

Take the series $(-1)^{n-1} B_n$, where $B_n$ is positive. Determine if the series is convergent or divergent based on if $B_{n+1} \leq B_n$ and $\lim_{{n \to \infty}} B_n = 0$.

Apply the alternating series test to different series to determine convergence or divergence: $(-1)^n \cdot \frac{3n-1}{2n+1}$ and $(-1)^{n+1} \cdot \frac{n^2}{n^3+4}$.

Given an alternating series $\sum (-1)^{n-1} \frac{1}{n}$, determine if the series converges using the Alternating Series Test.

Determine if the series $\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{4n-1}$ converges using the alternating series test.

Determine if the series $\sum_{n=1}^{\infty} \frac{1}{\sqrt{2n+1}}$ converges using the alternating series test.

Approximate the sum of the series $\frac{(-1)^{n+1}}{n^2}$ correct to two decimal places.

Approximate the sum of the series $(-1)^{n+1}/n^3$ correct to three decimal places.

Determine the interval of convergence for the series $\sum_{n=0}^{\infty} \frac{(-1)^n x^n}{4^{n+1}}$.

Find the sum $\sum_{n=0}^{\infty} \frac{(-1)^n \pi^{2n+1}}{4^{2n+1} (2n+1)!}$ and evaluate it.

Find the sum $\sum_{n=0}^{\infty} \frac{(-1)^n \pi^{2n+1}}{3^{2n-2} (2n)!}$.