Question

Consider the following geometric series.

Answer 1

Answer:

1. |r| = 1/4. or 0.25

2. Since r < 1, the geometric series is convergent.

3. To obtain the sum, we consider the formula of obtaining the sum to infinity of a geometrical series;

S = a /(1 - r)

where a = 2 ( first term)

r = 0.25 ( common ratio)

Therefore:

S = 2 /( 1 - 0.25)

= 2 / 0.75

= 8/3 or 2.6667

Hence, the sum is 8/3