# Binomial Coefficients Calculator

An easy to use calculator that calculates the binomial coefficients $ {n\choose k} $ from k= 0 to k = n included in the binomial theorem expansion.
## Use of the Binomial Coefficients CalculatorEnter the exponent $n$ as a positive integer greater than 1 and press "Expand". The outputs are the coefficients $ {n\choose k} $ from k = 0 to k = n.## Binomial Theorem Expansion and the Binomial CoefficientsThe binomial coefficients ${n\choose k}$ that the above calculator compute are included in the binomial expansion theorem formula as follows. $$(a x + b y)^n = \sum_{k=0}^{n} {n\choose k} (a x)^{n-k} (a y)^k$$ Example$(2 x - 3 y)^3 = \sum_{k=0}^{3} {3\choose k} (2 x)^{3-k} (-3 y)^k$ $ = {3\choose 0} (2 x)^{3-0} (-3 y)^0 + {3\choose 1} (2 x)^{3-1} (-3 y)^1 + {3\choose 2} (2 x)^{3-2} (-3 y)^2 + {3\choose 3} (2 x)^{3-3} (-3 y)^3$ ## More References and linksBinomial Theorem Expansion Calculators.Maths Calculators and Solvers. |