Math Tools

Root Test Calculator

by The Scientific Place

∑n=N∞\sum_{n=N}^{\infty}

The following series will be tested:

∑n=N∞2nn\sum_{n=N}^{\infty} \frac{2^{n}}{n}

The following is the test result:

Click "Test" to begin. \text{Click "Test" to begin.}
What is the Root Test?

The Root Test is a test used to tell whether an infinite series converges or diverges. Suppose that we have an infinite series ∑an\sum{a_n}. If the limit L=lim⁡n→∞∣an∣1nL = \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.

What does an inconclusive result mean?

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

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