CO22 The Binomial Theorem

The binomial theorem gives the expansion of (x+y)^n in terms of binomial coefficients. It is a powerful tool for proving identities for binomial coefficients. We state and prove the binomial theorem and give applications to finding binomial identities.

Earlier videos in this series introduced binomial coefficients and their properties:
CO16 Counting Combinations via Binomial Coefficients CO16 Counting subsets aka Combination...
CO18 Counting Combinations with repetitions
CO19 Combinatorial Proofs of Binomial Identities CO19 Combinatorial Proofs of Binomial...
CO20 Unimodality of Binomial Coefficients CO20 Unimodality of Binomial Coeffici...
CO21  Bounds for Ramsey Numbers (using binomial coefficients) CO21 Upper and Lower Bounds for Ramse...

A series of lectures on introductory Combinatorics. This full course is based on my book
Shahriar Shahriari, An Invitation to Combinatorics, Cambridge University Press, 2022.
DOI: https://doi.org/10.1017/9781108568708

For an annotated list of available videos for Combinatorics see
https://pomona.box.com/s/by2ay2872avx...
YouTube Playlist: Combinatorics, An Invitation

Shahriar Shahriari is the William Polk Russell Professor of Mathematics at Pomona College.

Subscribe to my channel  @Shahriari