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The General Binomial Theorem and Power Approximations

12th Grade · Math · Open Global Math

6 lessons

Goal

Expand binomial expressions for positive integers and generalize to rational exponents with convergence criteria to approximate numerical and functional values.

6 lessons
0 of 6 done
  1. Binomial Expansions for Positive Integers and CombinatoricsUp next
  2. Finding Specific Terms and Coefficients in Binomial ExpansionsNot started yet
  3. The Extended Binomial Theorem for Rational ExponentsNot started yet
  4. Expanding General Binomials with Rational PowersNot started yet
  5. Validity Intervals and Convergence Criteria for Binomial SeriesYou are here
  6. Numerical and Functional Approximations Using Binomial SeriesNot started yet
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Learning standards covered

GlobalOGM.13.NUM.4Open Global Math Standards 2026™ · 12th Grade

Expand binomial expressions $(a + bx)^n$ using factorial notation and combinations $\binom{n}{r}$ for positive integers, and generalize to rational exponents $n \in \mathbb{Q}$ with convergence criterion $|\frac{bx}{a}| < 1$ to approximate numerical and functional values.