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Fungrim entry: 5d6f99

(nk)≤(ne)kkk{n \choose k} \le \frac{{\left(n e\right)}^{k}}{{k}^{k}}
Assumptions:n∈Z≥0  and⁡  k∈Z≥0n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}
TeX:
{n \choose k} \le \frac{{\left(n e\right)}^{k}}{{k}^{k}}

n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Binomial(nk){n \choose k} Binomial coefficient
Powab{a}^{b} Power
ConstEee The constant e (2.718...)
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("5d6f99"),
    Formula(LessEqual(Binomial(n, k), Div(Pow(Mul(n, ConstE), k), Pow(k, k)))),
    Variables(n, k),
    Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(k, 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.

2021-03-15 19:12:00.328586 UTC