#### CHECK OUT SHMOOP'S FREE STUDY TOOLS: Essay Lab | Math Shack | Videos

# Series

# Series Topics

## Series explanations, examples, practice problems. Ready? Let’s do this.

#### Series: This is the Sum That Doesn't End

If you've never heard "The Song the Doesn't End", don't follow this link, we dare you.Never-ending series are much less annoying and much more useful. We promise.A series is a sum of numbers such a...

#### Alternating Series

An alternating series is a series whose terms alternate between positive and negative like a light switch being flipped on and off. Just like alternating sequences, the terms of such a series usual...

#### Convergence of Series

Now that we know how to bake an infinite brownie, we want to know what it tastes like. We are going to need to find a cow big enough to give us a glass of milk to match.In terms of series, this mea...

#### Math-e-magics?

We didn't use our psychic powers to figure out how the sequence of partial sums of a series is related to the terms of the series. Take a look at our first "mathic" trick."If the sequence of partia...

#### Properties of Series

A Match Made in Math-HeavenIf series are peanut butter, then integrals are jelly. You could put one or the other on a couple slices of bread and have a satisfying sandwich. You could also put them...

#### Special Cases

Every sport has its standouts. Some notables include professional Chessboxer Andy 'The Rock' Costello, toe wresting champion Paul 'Predatoe' Beech, and korfball all star Amy Turner. Math has its al...

#### Word Problems

Since arithmetic and geometric series are common menu items that everyone loves, they show up a lot in word problems. Unlike hotdogs and burgers, the word problems usually provide some individual q...

#### Visualization of Series

We've already mentioned that series and integrals are much alike. The integral is the series' brother from another mother. Before we put on our x-ray glasses and take a closer look at convergence a...

#### Tests for Convergence

Techniques that let you tell whether a series converges are unimaginatively called tests for convergence or convergence tests. Fortunately for us, we can equate them to Pandora's box. Pandora's box...

#### Taylor and Maclaurin Series

Right when we thought we had seen it all, it's time to take a look at the big boys: Taylor and Maclaurin. We like old Brook and Colin, they made calculus class just a little bit easier—at least w...

#### In the Real World

We've seen that geometric series can get used to calculate how much money you've got in the bank. They can also be used to calculate the amount of medicine in a person's body, if you know the dosin...