Infinite Decimal Expansion as an Infinite Series

Define a function $p(n)$ which takes a nonnegative integer $n$ and returns the $n^{th}$ digit of $\pi$, with the ones place being thought of as the "zeroth" digit. For example, $p(0) = 3$, $p(1) = 1$, $p(2) = 4$, and so on. With this definition, which of the following series are equal to $\pi$?