# Series

13 videos

3 skills

You're familiar with sequences and have been eager to sum them up. Well wait no longer! In this tutorial, we'll see that series are just sums of sequences and familiarize ourselves with the notation.

### Sigma notation for sums

VIDEO
4:27 minutes

### Introduction to geometric series

VIDEO
2:53 minutes

Think about a geometric series as the sum of a geometric sequence.

### Writing a series in sigma notation

VIDEO
3:16 minutes

### Explicitly defining a series

VIDEO
4:25 minutes

### Formula for arithmetic series

VIDEO
7:47 minutes

### Evaluating finite arithmetic series

PRACTICE PROBLEMS

Find the sum of the first n terms of an arithmetic sequence.

### Finding the sum of n squares part 1

VIDEO
6:16 minutes

### Finding the sum of n squares part 2

VIDEO
5:12 minutes

### Alternate formula for sum of n squares

VIDEO
4:51 minutes

### Using properties of series to find a sum

VIDEO
6:54 minutes

Watch Sal use the properties of sigma notation to make a difficult problem easy!

### Challenge: Sigma notation properties

PRACTICE PROBLEMS

Test yourself on some tricky properties of sigma notation.

### Infinite series as limit of partial sums

VIDEO
4:48 minutes

Infinite series as limit of partial sums

### Partial fraction decomposition to find sum of telescoping series

VIDEO
12:31 minutes

### Divergence of telescoping series

VIDEO
4:53 minutes

### Convergence and divergence of series

PRACTICE PROBLEMS