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

question 37

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