To find the value of A, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

where S is the sum of the series, a is the first term, and r is the common ratio.

In this case, the first term a is 1 and the common ratio r is 1/2. Therefore, we have:

A = 1 / (1 - 1/2)

Simplifying the expression, we get:

A = 1 / (1/2)

To divide by a fraction, we can multiply by its reciprocal:

A = 1 * (2/1)

A = 2

Therefore, the value of A is 2.