# Geometric Series

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Examples, solutions, videos, worksheets, and activities to help Algebra II students learn about geometric series.

What is a Geometric Series?
We can use what we know of geometric sequences to understand geometric series. A geometric series is a series or summation that sums the terms of a geometric sequence. There are methods and formulas we can use to find the value of a geometric series. It can be helpful for understanding geometric series to understand arithmetic series, and both concepts will be used in upper-level Calculus topics.

The following diagrams give the formulas for the partial sum of the first nth terms of a geometric series and the sum of an infinite geometric series. Scroll down the page for more examples and solutions of geometric series. Geometric Series Introduction
How to determine the partial sums of a geometric series?
Examples:
Determine the sum of the geometric series.
a) 3 + 6 + 12 + … + 1536
b) an 2(-3)n-1, n = 5

Geometric Series
Examples:

1. Evaluate for the specified number of terms:
1 + 3 + 9 + …; n = 7
2. Does this series have a sum?
120 + 60 + 30 + …
3. Does this series have a sum?
5 + 15 + 45 + …

How to determine if an infinite geometric series converges or diverges?
Example:
Determine if the series converges or diverges.
8 + 8/3 + 8/9 + 8/27 + 8/81 + …

Infinite Geometric Series
Examples:
Evaluate the infinite geometric series:
3 + 1/3 + 1/27 + …
Is the series arithmetic or geometric? Evaluate for the specified number of terms.
-3 + 12 - 48 + …; n = 6

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