- #1
- 12,175
- 182
According to this link at Wolfram, the following formula can be used to calculate any digit of the base-16 representation of π:
[tex]
\pi = \sum_{n=0}^{\infty} \
\left(
\frac{4}{8n+1} - \frac{2}{8n+4} - \frac{1}{8n+5} - \frac{1}{8n+6}
\right)
\cdot \frac{1}{16^n}
[/tex]
But apparently it is not as straightforward as simply taking the nth term in the series to get the nth digit. For example, the 0th term is 3.1333..., and not simply 3 as it must be.
So my question is, just how does one use this formula to calculate a digit? Or am I missing something in my above reasoning?
[tex]
\pi = \sum_{n=0}^{\infty} \
\left(
\frac{4}{8n+1} - \frac{2}{8n+4} - \frac{1}{8n+5} - \frac{1}{8n+6}
\right)
\cdot \frac{1}{16^n}
[/tex]
But apparently it is not as straightforward as simply taking the nth term in the series to get the nth digit. For example, the 0th term is 3.1333..., and not simply 3 as it must be.
So my question is, just how does one use this formula to calculate a digit? Or am I missing something in my above reasoning?