# Sequences, series and induction

Contents

An assortment of concepts in math that help us deal with sequences and proofs.

## Arithmetic sequences

Review arithmetic sequences before you dive into arithmetic series.

## Basic sigma notation

Learn how to use and interpret sigma notation. Hint: It means take the sum!

## Finite arithmetic series

Learn how to evaluate and work with finite arithmetic series.

## Geometric sequences

Review geometric sequences before you dive into geometric series.

## Finite geometric series

Whether you are computing mortgage payments or calculating how many users your website will have after a few years, geometric series show up in life far more than you imagine. This tutorial will review all the important concepts and more!

## Finite geometric series applications

Apply what you've learned about geometric series to model situations in some fun word problems.

## Advanced sigma notation

Now that you know basic sigma notation and series, we can put the two together to write series using sigma notation and evaluate more challenging expressions.

## Infinite geometric series

You're already familiar with finite geometric series, but you don't want the summation to stop!! What happens if you keep adding? The terms are getting small fast! Can it be that the sum of an infinite number of rapidly shrinking terms can be finite! Yes, often times it can! Mind-blowing! Stupendous!

## Infinite geometric series applications

Apply what you've learned about infinite geometric series to model situations in some fun word problems.

## Deductive and inductive reasoning

You will hear the words "deductive reasoning" and "inductive reasoning" throughout your life. This very optional tutorial will give you context for what these mean.

## Induction

Proof by induction is a core tool. This tutorial walks you through the general idea that if 1) something is true for a base case (say when n=1) and 2) if it is true for n, then it is also true for n+1, then it must be true for all n! Amazing!