Working with Geometric Series

#10.2 Working with Geometric Series

Welcome to the first of many convergence tests that you will learn called the geometric series test! But before we start, we’ll go over what exactly a geometric series is and the significance of having one!

If you would like a review of what a convergent vs. divergent infinite series is, check out our 10.1 guide: Defining Convergent and Divergent Infinite Series!

#🔺 What is a Geometric Series?

A geometric series is a series that follows the standard format as shown below. Pay attention to the difference in where the sequence starts! The first series starts from 0 and the second series starts from 1!

$$s_n = \sum_{n=0}^{\infty} a \cdot r^n$$

$$s_n = \sum_{n=1}^{\infty} a \cdot r^{n-1}$$

The definition of a geometric series is a series with a constant ratio between successive terms. Therefore $a$ is your initial term and $r$ is the ratio between any two consecutive terms!

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