How do I write the following finite series as a sum or product:
$$f\left(k\right) = {1 \over p_1} \left(1 + {1 \over p_2} \left(1 + {1 \over p_3}\left(1+\dots \right) \right) \right)$$
…all the way up to $p_k$, the $k$th prime? $p_1 = 2$.
Also, how can I actually solve it for a given (large) $k$, without loosing precision due to floating point arithmetic?