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Fungrim entry: 433d8b

(2nn)<4nπn{2 n \choose n} < \frac{{4}^{n}}{\sqrt{\pi n}}
Assumptions:n∈Z≥1n \in \mathbb{Z}_{\ge 1}
TeX:
{2 n \choose n} < \frac{{4}^{n}}{\sqrt{\pi n}}

n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
Binomial(nk){n \choose k} Binomial coefficient
Powab{a}^{b} Power
Sqrtz\sqrt{z} Principal square root
Piπ\pi The constant pi (3.14...)
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("433d8b"),
    Formula(Less(Binomial(Mul(2, n), n), Div(Pow(4, n), Sqrt(Mul(Pi, n))))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(1))))

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2021-03-15 19:12:00.328586 UTC