Khan Academy on a Stick
Sequences and induction
An assortment of concepts in math that help us deal with sequences and proofs.

Proof by Induction
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Proving an expression for the sum of all positive integers up to and including n by induction

Alternate Proof to Induction for Integer Sum
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Another way to prove the expression for the sum of all positive integers up to and including n
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!

Explicit and recursive definitions of sequences
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 Arithmetic sequences

Finding the 100th Term in a Sequence
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Finding the 100th Term in a Sequence

Equations of Sequence Patterns
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Equations of Sequence Patterns

Geometric sequences introduction
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An introduction to geometric sequences
 Geometric sequences
 Converting an explicit function to a recursive function

Sum of arithmetic sequence (arithmetic series)
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 Formula for arithmetic series
Basic sequences and series
This sequence (pun intended) of videos and exercises will help us explore ordered lists of objectseven infinite onesthat 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.

Difference between inductive and deductive reasoning
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Deductive Reasoning 1

Deductive Reasoning 2
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Deductive Reasoning 2

Deductive Reasoning 3
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Deductive Reasoning 3

Inductive Reasoning 1
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Inductive Reasoning 1

Inductive Reasoning 2
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Inductive Reasoning 2

Inductive Reasoning 3
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Inductive Reasoning 3

Inductive Patterns
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Inductive Patterns
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.
 Convergent and divergent sequences

Definition of limit of a sequence and sequence convergence
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 Proving a sequence converges
 Series as sum of sequence
 Formula for finite geometric series

2003 AIME II Problem 8
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Sequence from the product of 2 arithmetic sequences

Advanced: Geometric series sum to figure out mortgage payments
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Figuring out the formula for fixed mortgage payments using the sum of a geometric series

Series Sum Example
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2010 IIT JEE Paper 1 Problem 54 Series Sum
Advanced sequences and series
You understand what sequences and series are and the mathematical notation for them. This tutorial takes things further by exploring ideas of convergence divergence and other, more challenging topics.