Fungrim home page

Fungrim entry: 6b3af0

(nk)nkk!{n \choose k} \le \frac{{n}^{k}}{k !}
Assumptions:nZ0andkZ0n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, k \in \mathbb{Z}_{\ge 0}
TeX:
{n \choose k} \le \frac{{n}^{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
Factorialn!n ! Factorial
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("6b3af0"),
    Formula(LessEqual(Binomial(n, k), Div(Pow(n, k), Factorial(k)))),
    Variables(n, k),
    Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(k, ZZGreaterEqual(0)))))

Topics using this entry

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

2019-08-17 11:32:46.829430 UTC