Review Question 12: Binomial Series

In this video I over a quick recap on the binomial series, its radius of convergence, and its binomial coefficients. A binomial series is an infinite series for the function (1 + x)ⁿ where k is any real number and the series is convergent when the absolute value of x is less than 1. The terms of the series consist of the binomial coefficients multiplied by xⁿ. The binomial coefficients, often pronounced as "k choose n", have the formula k! / (n! (k - n)!, and represent the number of was to choose n elements from a set of k. For example, 4 choose 2 = 6 ways to choose 2 numbers from a set of 4 numbers: {1, 2}, {1,3}, {1,4}, {2,3}, {2,4}, and {3,4}.

The timestamps of key parts of the video are listed below:

• Question 12: Binomial Series 0:00
• Solution: 0:15
• Binomial coefficients: 2:03
• n choose 3 binomial coefficient example: 2:30

This video was taken from my earlier video listed below:

• Infinite Sequences and Series: Review and True-False Quiz: https://youtu.be/F0dsQLdXXpI
• HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-review-and-true-false-quiz
• Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FCqXVJv1r7eJvrvphfkr6L

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Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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