ALGEBRA & NUMBER THEORY

Binomial Theorem

Expands binomial sums raised to integer powers into finite sums.

(a+b)n=∑k=0n(nk)an−kbk(a+b)^n=\sum_{k=0}^{n}\binom{n}{k}a^{n-k}b^k

symbols, variables and units

a, b: commutable numbers or quantities; n, k: dimensionless integers.

applicable conditions and boundaries

n is a non-negative integer; non-integer powers require generalized series and convergence conditions.

formula source code

The following is a copyable LaTeX expression.

(a+b)^n=\sum_{k=0}^{n}\binom{n}{k}a^{n-k}b^k

Reference and Extended Learning

OpenStax · Algebra and Trigonometry ↗

is organized according to model definition and assumptions. Please check actual conditions and original literature before engineering, research and clinical use.

binomial theoremcombination number

Same subject formula

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