Question

The sum of the infinite geometric series with a first term of 2 and a common ratio of 1/2 is?

Answer 1

Hi there!

We can use the equation:

$s = \frac{a}{1-r}$

a = initial term

r = common ratio

s = sum

Plug in the given values:

$s = \frac{2}{1-\frac{1}{2}} = \frac{2}{\frac{1}{2}} = \boxed{4}$

Answer 2

Answer:

S∞ = 4

Step-by-step explanation:

The sum to infinity of a geometric sequence is

S∞ = $\frac{a}{1-r}$ ; | r | < 1

where a is the first term and r the common ratio

Here a = 2 and r = $\frac{1}{2}$ , then

S∞ = $\frac{2}{1-\frac{1}{2} }$ = $\frac{2}{\frac{1}{2} }$ = 4