Fungrim home page

Fungrim entry: fa3b53

(nk)2n{n \choose k} \le {2}^{n}
Assumptions:nZ0  and  kZ0n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}
{n \choose k} \le {2}^{n}

n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}
Fungrim symbol Notation Short description
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:
    Formula(LessEqual(Binomial(n, k), Pow(2, n))),
    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.

2020-04-08 16:14:44.404316 UTC