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!

Partial sum notation

VIDEO 6:09 minutes
Partial sum notation

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