$\sum_{n=N}^{\infty}$

The following series will be tested:

$\sum_{n=N}^{\infty} \frac{2^{n}}{n}$

The following is the test result:

$\text{Click "Test" to begin.}$

The Root Test is a test used to tell whether an infinite series converges or diverges. Suppose that we have an infinite series $\sum{a_n}$. If the limit $L = \lim_{n\to\infty}{|a_n|^{\frac{1}{n}}}$ is less than 1, the series converges. If it is greater than 1, the series diverges. Otherwise, the test is inconclusive.

An inconclusive result happens when the limit mentioned in the first question, $L$, is either 1 or DNE. In that case, the Root Test cannot tell you whether that series converges or diverges.