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!
This sequence (pun intended) of videos and exercises will help us explore ordered lists of objects--even infinite ones--that often have some pattern to them. We will then explore constructing sequences where the nth term is the sum of the first n terms of another sequence (series). This is surprisingly useful in a whole series (pun intended) of applications from finance to drug dosage.
What happens when the ratio between successive terms in a sequence is the same (or it has a "common ratio")? Well, then we'd be dealing with a geometric sequence (which comes up extremely frequently in mathematics).
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!
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!