Geometric Series - Formula, Examples, Convergence

Before knowing the geometric series formula, let us recall what is a geometric series. It is a series (sum of terms) where the ratios of every two consecutive terms are the same. The geometric series formula includes:Formula to find the nth term of a geometric series.Finding the sum of a finite geometric series.Finding the sum of an infinite geometric series.What is a Geometric Series?A geometric series is the sum of finite or infinite terms of a geometric sequence. For the geometric sequence a, ar, ar2, ..., arn-1, ..., the corresponding geometric series is a + ar + ar2 + ..., arn-1 + .... We know that "series" means "sum". In particular, the geometric series means the sum of the terms that have a common ratio between every adjacent two of them. There can be two types of geometric series: finite and infinite. Here are some examples of geometric series.1/2 + 1/4 + .... + 1/8192 is a finite geometric serieswhere the first tern, a = 1/2 and the common ratio, r = 1/2-4 + 2 - 1 + 1/2 - 1/4...