# Geometric Series Examples

### Example 1

Find the sum of the infinite geometric series given by: . Simplify and solve for the sum. | |

Locate r to make sure |*r*| < 1 to prove the geometric series converges.
Use the formula for the sum of an infinite geometric series. Substitute for *a*_{1} and *r* in the formula. | |

### Example 2

Find the sum of the infinite geometric series given by: . | |

*r* = 3
This series diverges because |*r*| ≥ 1. Therefore the sum is infinite. | |

### Example 3

Find the sixth partial sum of the geometric series given by: . Simplify the equation to solve for the sixth partial sum. | |

Use the formula for the partial sum of a geometric series. Substitute the values you know into the formula. | |

### Example 4

Find the sum: . Simplify the equation to solve for the third partial sum. | |

Use the formula for the partial sum of a geometric series. Substitute the values you know into the formula. | |

### People who Shmooped this also Shmooped...