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I have trouble understanding how to apply the BBP formula, i.e. actually compute the n-th digit of pi.

[itex]\pi[/itex]=[itex]\sum[/itex][itex]\frac{1}{16^{k}}[/itex]([itex]\frac{4}{8k+1}[/itex]-[itex]\frac{2}{8k+4}[/itex]-[itex]\frac{1}{8k+5}[/itex]-[itex]\frac{1}{8k+6}[/itex])

where the sum uses k from 0 to ∞.

I've read a few explanations how to adapt it, but have always failed to understand the following issues:

1) what is should be the expected returned value, i.e. what should I extract from it to get my n-th digit (I expect something fractional like [itex]\frac{p}{q}[/itex])?

2) what should I do with the infinite part of the sum? It seems illogical to me to approximate it somehow, since I expect the exact value of the desired digit

3) the above formula is supposed to calculate the hexadecimal formula of [itex]\pi[/itex]. What does that mean for the calculated digit? Is in that case the fractional part of [itex]\pi[/itex] regarded as a hexadecimal number?

Basically, I'm looking for an explanation how to apply the above formula and would be very thankful if someone of you could provide this explanation or a suitable link.

I'm not a professional mathematician, I'm an engineer, so I apologize in advance for any "foolish" questions/statements or if I've misplaced the question on the wrong forum.

Thanks for your understanding.

Regards

scienalc