Binomial series ( $(1 + x)^{α}$ )

For

∣ x ∣ < 1

, the binomial series is

(1 + x)^{α} = \sum_{n = 0}^{\infty} (n α) x^{n}, (n α) = \frac{α ( α - 1 ) \dots ( α - n + 1 )}{n !} .

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- Negative binomial series Binomial series

Negative binomial series ( $\sum_{k \geq 0} (k L + k) z^{k} = (1 - z)^{- L - 1}$ )

For a nonnegative integer

L

and

∣ z ∣ < 1

, this specialization of the binomial series sums the normalizing coefficients of a negative binomial distribution.

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Negative binomial series
Past exam of the mathematics course of the University of Cambridge / 2016 / ib / Paper 1 / 20H / c / Solution
Past exam of the mathematics course of the University of Cambridge / 2019 / ia / Paper 4 / 9A / c / Solution
Past exam of the mathematics course of the University of Cambridge / 2020 / ib / Paper 1 / 12G / Solution
Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 3 / 7E / i / Solution

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Binomial series by

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The binomial series is a way to express the expansion of a binomial expression raised to a power. Specifically, it provides the expansion of the expression \((a + b)^n\) for any real (or complex) number \(n\).

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