Question

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

Answer 1

S∞ = 4

Explanation:

The sum to infinity of a geometric sequence is

S∞ =
`(a)/(1-r)` ; | r | < 1

where a is the first term and r the common ratio

Here a = 2 and r =
`(1)/(2)` , then

S∞ =
`(2)/(1-(1)/(2) )` =
`(2)/((1)/(2) )` = 4

Answer 2

Hi there!

We can use the equation:

`s = (a)/(1-r)`

a = initial term

r = common ratio

s = sum

Plug in the given values:

`s = (2)/(1-(1)/(2)) = (2)/((1)/(2)) = \boxed{4}`