# Sum of Geometric Series

Until now, I can’t really memorize the formula of sum of geometric series. But don’t worry I know how to derive the formula. Don’t be like me; memorizing the formula by heart is always an advantage for you. If you are doing a constant practice about series and progression you will earn one very important skill. That is to read what is going on inside the dots.

Consider the geometric progression

Expressing the series to its sum(S_{n}) we have,

(1)

Multiplying r to both sides of equation we have,

(2)

(2)-(1):

–

From the term of (1) cancels out leaving the following

By common factor,

**Sample Problem 1:**

Find the sum of the following

Solution:

Let (1)

(2)

(2)-(1)

–

**Sample Problem 2:**

Find the sum of the series

This time let’s use our formula:

Where a=3, r=3, n=9

### Dan

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