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Fungrim entry: dea83d

π=limn4n2k=0nn2k2\pi = \lim_{n \to \infty} \frac{4}{{n}^{2}} \sum_{k=0}^{n} \sqrt{{n}^{2} - {k}^{2}}
\pi = \lim_{n \to \infty} \frac{4}{{n}^{2}} \sum_{k=0}^{n} \sqrt{{n}^{2} - {k}^{2}}
Fungrim symbol Notation Short description
Piπ\pi The constant pi (3.14...)
SequenceLimitlimnaf(n)\lim_{n \to a} f(n) Limiting value of sequence
Powab{a}^{b} Power
Sumnf(n)\sum_{n} f(n) Sum
Sqrtz\sqrt{z} Principal square root
Infinity\infty Positive infinity
Source code for this entry:
    Formula(Equal(Pi, SequenceLimit(Mul(Div(4, Pow(n, 2)), Sum(Sqrt(Sub(Pow(n, 2), Pow(k, 2))), For(k, 0, n))), For(n, Infinity)))))

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2021-03-15 19:12:00.328586 UTC