Beyond the Binomial Theorem: The Binomial Series
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In this video we will be building up to the Binomial Series. We start with Pascal's Triangle, whose coefficients are found in the expansion for powers of binomials. We then take a combinatorial approach to come up with the Binomial Theorem which applies to positive integer powers of binomials. But what if the exponent is some other real number? Well we can use the power of Taylor Series to come up with the Binomial Series, and along the way we define a natural extension of the "n choose k" notation that work for arbitrary real numbers too.
0:00 Pascal's Triangle
0:51 Expanding Binomials with Maple Calculator
2:00 Connecting Coefficients to Pascal's Triangle
4:03 Combinatorical Approach to Binormial Coefficients
5:12 Binomial Theorem
6:23 Extending "n choose k" formula
8:22 Taylor Series Review
10:00 The Binomial Series
11:22 Binomial Series in Maple Learn
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