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Fungrim entry: e1e106

π=limk16kk(2kk)2\pi = \lim_{k \to \infty} \frac{{16}^{k}}{k {{2 k \choose k}}^{2}}
TeX:
\pi = \lim_{k \to \infty} \frac{{16}^{k}}{k {{2 k \choose k}}^{2}}
Definitions:
Fungrim symbol Notation Short description
ConstPiπ\pi The constant pi (3.14...)
SequenceLimitlimnaf ⁣(n)\lim_{n \to a} f\!\left(n\right) Limiting value of sequence
Powab{a}^{b} Power
Binomial(nk){n \choose k} Binomial coefficient
Infinity\infty Positive infinity
Source code for this entry:
Entry(ID("e1e106"),
    Formula(Equal(ConstPi, SequenceLimit(Div(Pow(16, k), Mul(k, Pow(Binomial(Mul(2, k), k), 2))), k, Infinity))))

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

2019-08-17 11:32:46.829430 UTC