[seqfan] formula for Pi

[Alexander Povolotsky]

I've got this very ugly formula by playing Maple syntax via old and
new inverse symbolic calculators :

Pi = 6/7*(1/3*sum((843*n + 4607)/((n+5)*(3*n+7)*(3*n+22)),n=0...infinity)
 - 655999/248976  - 7/2*ln(3))*sqrt(3)

What I've got for Pi above - is it just a good approximation or exact ?
(My old PC with PARI/GP can not get over the summing )

It looks that this 655999/248976 fraction quickly becomes periodic around
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gp > \p 1000
realprecision = 1001 significant digits (1000 digits displayed)
gp > 1.0*655999/248976
%4 = 2.6347880
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Cheers Alexander R. Povolotsky