scienalc
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Hello everyone,
I have trouble understanding how to apply the BBP formula, i.e. actually compute the n-th digit of pi.
\pi=\sum\frac{1}{16^{k}}(\frac{4}{8k+1}-\frac{2}{8k+4}-\frac{1}{8k+5}-\frac{1}{8k+6})
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 \frac{p}{q})?
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 \pi. What does that mean for the calculated digit? Is in that case the fractional part of \pi 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
I have trouble understanding how to apply the BBP formula, i.e. actually compute the n-th digit of pi.
\pi=\sum\frac{1}{16^{k}}(\frac{4}{8k+1}-\frac{2}{8k+4}-\frac{1}{8k+5}-\frac{1}{8k+6})
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 \frac{p}{q})?
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 \pi. What does that mean for the calculated digit? Is in that case the fractional part of \pi 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