# Geometric series

7 videos
2 skills
Whether you are computing mortgage payments or calculating the distance traveled by a bouncing ball, geometric series show up in life far more than you imagine. This tutorial will review all the important concepts and more!

### Introduction to geometric series with sigma notation

VIDEO 4:28 minutes
Sal extends the idea of geometric sequences to geometric series.

### Deriving the formula for the sum of a finite geometric series

VIDEO 9:38 minutes

### Evaluating finite geometric series

PRACTICE PROBLEMS
Evaluate finite geometric series given in sigma notation, recursively, or explicitly.

### Another derivation of the sum of an infinite geometric series

VIDEO 4:46 minutes
Sal applies limits to the formula for the sum of a finite geometric series to get the sum of an infinite geometric series.

### Deriving the sum of an infinite geometric series

VIDEO 7:54 minutes

### Examples: Converging and diverging geometric series

VIDEO 4:16 minutes
Sal looks at three different infinite geometric series and determines if each of them converges or diverges.

### Repeating decimal as infinite geometric series

VIDEO 8:02 minutes
See how we can write a repeating decimal as an infinite geometric series.

### Vertical distance of bouncing ball

VIDEO 5:10 minutes
Watch Sal determine the total vertical distance a bouncing ball moves using an infinite geometric series.

### Evaluating infinite geometric series

PRACTICE PROBLEMS
Find the sum of an infinite geometric series, but only if it converges!