Answer :
Answer:
The sum of the series is 3/2
Step-by-step explanation:
Given
1 + 1/3 + 1/3^2 + ....
Required
The sum of the series
This implies that we calculate the sum to infinity.
We have:
[tex]a = 1[/tex] -- The first term
First, calculate the common ratio (r)
[tex]r = \frac{1}{3^2} / \frac{1}{3}[/tex]
Change to product
[tex]r = \frac{1}{3^2} * \frac{3}{1}[/tex]
Solve
[tex]r = \frac{1}{3}[/tex]
The sum of the series is then calculated as:
[tex]S_{\infty} = \frac{a}{1 - r}[/tex]
[tex]S_{\infty} = \frac{1}{1 - 1/3}[/tex]
Solve the denominator
[tex]S_{\infty} = \frac{1}{2/3}[/tex]
Express as product
[tex]S_{\infty} = 1 * \frac{3}{2}[/tex]
[tex]S_{\infty} = \frac{3}{2}[/tex]