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Math

Geometric Series

A geometric series is the sum of the terms of a geometric sequence. General form of a geometric series is given by:

Sum of the first n terms of a geometric series is given by:

                                                                                     

Example: Find the sum of the first 10 terms of the following geometric series:

For the above geometric series the common ratio is:

Using the formula for the sum of the series we find:

 

Example: Find the sum of the first n terms of the following geometric series:

 

We can find the common ratio for this series:

The nth term of the series is:

We can solve the above equation to find the number of terms of the series:

In the above equation we used  Therefore, the series has twelve terms. So, we find:

 

 

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