Mathematics Challenges -1

$S = \sum _{ x=1 }^{ \infty }{ \frac { { \zeta }{ \left( 2x \right) } }{ { \Gamma }{ \left( { x }+{ \frac { 1 }{ 2 } } \right) } } }$

Find $\lfloor 1000S \rfloor$ .

Notations:

• $\zeta (\cdot)$ denotes the Riemann zeta function.
• $\Gamma (\cdot)$ denotes the gamma function