# Alternating Series

The alternating series test is a type of series test used to determine the convergence of alternating series. In this step-by-step guide, you will learn more about the alternating series.

## A step-by-step guide toalternating series

An alternating series is a series in which the terms alternate between positive and negative. The general form of an alternating series is as follows:

$$\color{blue}{\sum \:\left(-1\right)^ka_{k}}$$

Where $$a_{k}\ge 0$$ and the first index is arbitrary. It means that the starting term for an alternating series can have any sign.

We can say that an alternating series $$[a_k]^\infty_{k=1}$$ converges if two conditions exist:

• $$0\le a_{k+1}\le a_k$$, for all $$k\ge 1$$
• $$a_k→0$$, as $$k→+∞$$

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