[Updated 3.15 with this delicious photo and comment.]
From Iowahawk on Twitter (@iowahawkblog)
Correction: Happy lim[n→∞] 2^4n / (n * (2n! / (2*(n!)))^2) Day
#PiDay How to bake your own converging pi in Excel:
- let cell A1 = value of n
- in cell B1, enter the formula =EXP(4*A1*LN(2) – LN(A1) – (2*(GAMMALN(2*A1+1) – 2* GAMMALN(A1+1))))
- enter larger and larger values for n in cell A1, or create a column series
And voila: convergence through n=20 #PiDay
[A small explanation]
@BunceHoratio it’s a handy dandy function for formulas that involve factorials.
n! = Gamma(n+1) = exp(ln(Gamma(n+1)), or in Excel parlance =exp(GammaLn(n+1))
[But there’s a problem via David Rinaldo @valid_android]
@iowahawkblog This breaks around n=20000000000000 says 2.7 (yes I know why)
[Mr. Hawk replies]
@Valid_Android Because Bill Gates is a punkass bitch
@triadaxiom Blame Microsoft’s shitty precision, not math
