How to get the sum to infinity of a geometric series

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4 years ago

In community: Mathematics Proofs(c46e)

In my last mathematical post I revealed how to get the general rule for the sum of a geometric series. In this article, I'll be demonstrating how to work with the general rule to come up with the sum to infinity of a geometric series.

When there is a sum to infinity of a geometric series - we can say it is convergent. 'Convergent' basically means the series will tend to a specific value as more terms are added to it.

Now, the sum to infinity of a geometric series will exist if these terms are met:

-1 < r < 1

Like written in the previous article:

a = First term

r = Common ratio

When you have the general rule:

S_n = [a(1-r^n)]/(1-r)

If -1 < r < 1, r^n -->0, as n-->∞

Therefore:

S_∞ = [a(1-0)]/(1-r) = a/(1-r)

When |r| < 1

In the two videos below, the mathematics above is explained clearly. These videos are worth watching if you haven't understood the mathematics yet.