I was recently interested in the formula
equ 1: $$\sum_{n=0}^∞ 1/2^n$$
This made me curious about:
equ 2: $$\sum_{n=0}^∞ \frac{1}{\pi^n}$$
I found that the second formula converges to 0.466942206924260.
Several google searches later, I couldn't find anything useful that referenced equ 2 beyond these two articles: article 1 and article 2.
Is there anything mathematically meaningful about equ 2 and its value?
By no means am I a mathematician :)
As mentioned by JMoravitz, the series in question is a geometric series and so its sum has a closed formula: $$ \sum_{n=0}^\infty \frac{1}{\pi^n} = \frac{1}{1-\pi^{-1}} = \frac{\pi}{\pi-1} \approx 0.466942206924260\cdots $$