Question

Sum of series 1 +1/3 +1/3².... is?​

Answer 1

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:

$a = 1$ -- The first term

First, calculate the common ratio (r)

$r = \frac{1}{3^2} / \frac{1}{3}$

Change to product

$r = \frac{1}{3^2} * \frac{3}{1}$

Solve

$r = \frac{1}{3}$

The sum of the series is then calculated as:

$S_{\infty} = \frac{a}{1 - r}$

$S_{\infty} = \frac{1}{1 - 1/3}$

Solve the denominator

$S_{\infty} = \frac{1}{2/3}$

Express as product

$S_{\infty} = 1 * \frac{3}{2}$

$S_{\infty} = \frac{3}{2}$