Calculus 2 | 22.1: The Binomial Series (1 + x)^k

Full course — free exercises, Feynman reviews, and AI-graded feedback: https://ludium.ai/courses/calculus-2 For weeks, every Maclaurin series meant grinding out derivative after derivative. The binomial series ends that: one formula expands (1 + x) to any power k, whether k is a fraction, a negative, or a whole number. We derive it, name its coefficients, and walk away with a table of common series you can reuse forever. Key concepts covered: The general binomial series for (1 + x) to the power k Binomial coefficients and the "k choose n" symbol Why the series terminates when k is a positive integer (Pascal's Triangle) Convergence cases for the binomial series Expanding the square root of 1 + x as a power series A reusable table of common Maclaurin series ━━━━━━━━━━━━━━━━━━━━━━━━ SOURCE MATERIALS The source materials for this video are from    • Calculus 2 Lecture 9.8:  Representation of...