Calculus 2: Ratio and root tests

Use the ratio test to determine the convergence of the series $\frac{n^n}{n!}$.

Use the root test to determine if the series $\left(\frac{3+5n}{2+3n}\right)^n$ converges, diverges, or is inconclusive.

Apply the root test to the series $\left(\frac{1}{n^2 + \frac{1}{n}}\right)^n$.

Use the root test on the series $\left(\frac{n^n}{2^{1+4n}}\right)$ to determine its convergence or divergence.

Determine if the series $\displaystyle \left(\frac{n}{2^n}\right)$ converges or diverges using the root test.

Apply the root test to the series $(-1)^n \cdot \frac{3^{n+2}}{(n-1)^n}$ to determine if it converges or diverges.

Using the Ratio Test or the Root Test, determine if the infinite series $\sum a_n$ converges or diverges.

Using the ratio test, determine if a given series converges or diverges.

Apply the root test to check if a series converges absolutely or diverges.

Using the ratio or root test, determine if the series [{ "type" : "katexPlugin", "text": "\sum a_n", "inline": true }]', is absolutely convergent.