Inverse Prime Series

Calculus Level 3

$\large \dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{5}+\dfrac{1}{7}+\dfrac{1}{11}+\dfrac{1}{13}+\dfrac{1}{17}+\cdots$ $\large \dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{11}-\dfrac{1}{13}+\dfrac{1}{17}-\cdots$

The second series gives a finite result The first series gives a finite result Both series gives a finite result Both series explodes to infinity