Answer:
Convergent. The sum is 2.
Step-by-step explanation:
First let's find the rate of the series. We can find it by dividing one term by the term before:
[tex]0.5 / 1 = 0.5[/tex]
[tex]0.25 / 0.5 = 0.5[/tex]
[tex]0.125 / 0.25 = 0.5[/tex]
So the rate of the series is 0.5. The series is convergent if the rate is between 0 and 1, so this series is convergent.
We can find its sum with the following equation:
[tex]S = a_1 / (1 - r)[/tex]
Where a_1 is the first term and r is the rate.
So we have that:
[tex]S = 1/ (1 - 0.5)[/tex]
[tex]S = 2[/tex]
The sum of the series is 2.
