Determine the Sum of the Infinite Series $\sum _ { k = 0 } ^ { \infty } \left( \frac { 1 } { 2 } \right) ^ { 2 k }$

Multiple Choice

Determine the sum of the infinite series: $\sum _ { k = 0 } ^ { \infty } \left( \frac { 1 } { 2 } \right) ^ { 2 k }$ .

A) $\frac { 2 } { 3 }$
B) 2
C) $\frac { 4 } { 3 }$
D) $\frac { 4 } { 5 }$
E) none of these