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Fungrim entry: 858c8f

k=0n(nk)=2n\sum_{k=0}^{n} {n \choose k} = {2}^{n}
Assumptions:nZ0n \in \mathbb{Z}_{\ge 0}
TeX:
\sum_{k=0}^{n} {n \choose k} = {2}^{n}

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Sumnf ⁣(n)\sum_{n} f\!\left(n\right) Sum
Binomial(nk){n \choose k} Binomial coefficient
Powab{a}^{b} Power
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("858c8f"),
    Formula(Equal(Sum(Binomial(n, k), Tuple(k, 0, n)), Pow(2, n))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(0))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-21 11:44:15.926409 UTC