Without changing anything major, 40: 

$s+=1/$_**2for 1..1000000;print sqrt$s*6

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Note that neither this nor your solution is of arbitrary precision. Both are limited to double precision.

Update: 38: 

$s+=6/$_**2for 1..1000000;print sqrt$s

[download]

In reply to Re: Pi golf: by ikegami
in thread Pi golf: by Robbjedi

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