How do you find the sum of the infinite geometric series 1.02 + 2.04 + 4.08 + 8.16 +…?

Nov 14, 2015

You don't.

Explanation:

You can only find the sum of an infinite geometric series if the ratio between each term is between -1 and 1. Or, with more rigor,

$- 1 < r < 1$

In that case the formula for the sum would be

$\frac{{a}_{0} - {a}_{n} r}{1 - r}$

Where ${a}_{0}$ is the first term and ${a}_{n}$ is the nth term.

If $r$ is between -1 and 1, then ${a}_{n}$ will be so small you can disconsider it and find the infinite sum.