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Math — Binomial Theorem & Sequences

Binomial expansion, combinations, arithmetic and geometric series.

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

\binom{n}{k} = \frac{n!}{k!(n-k)!}

a_n = a_1 + (n-1)d

S_n = \frac{a_1(1-r^n)}{1-r}