Khan Academy on a Stick : Sequences and induction

Khan Academy on a Stick

Trigonometry and precalculus

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 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.

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.