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Binomial Theorem

★★★☆☆High School

📖Definition

A formula for expanding powers of binomials using combinations as coefficients.

(x + y)ⁿ = ∑_k=0ⁿ \binomnk x^n-k y^k

Binomial theorem

\binomn0 + \binomn1 + ·s + \binomnn = 2ⁿ

Sum of binomial coefficients

예제 1★★☆☆☆

Expand (x + 1)⁴.

Discovered by: Isaac Newton (17th century)

Newton generalized to negative/fractional exponents.

Binomial distribution derivation

(1+x)ⁿ approximations

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