binomial identity

Let x, y and n be real numbers that are not equal to zero. If left bracketing bar y/x right bracketing bar <1, then (x + y)^n = sum_(k=0)^∞ binomial(n, k) x^(n - k) y^k where binomial(n, k) = (n(n - 1)...(n - k + 1))/(k!). If n is a positive integer, then the coefficients can be written as binomial(n, k) = (n!)/(k!(n - k)!) and regardless of the value of the ratio left bracketing bar y/x right bracketing bar , the series terminates at n and is given by: (x + y)^n = sum_(k=0)^n binomial(n, k) x^(n - k) y^k

Taylor's theorem

Euclid | Isaac Newton | Blaise Pascal