Find the sum of \(\frac{1}{7}+\frac{2}{7^2}+\frac{1}{7^3}+\frac{2}{7^4}+...\)

Guest Jun 16, 2023

#2**0 **

The sum of the infinite series 1/7 + 2/7^2 + 1/7^3 + 2/7^4 + ... is 9/48.

This can be found using the formula for the sum of a geometric series:

S = a/(1-r)

where

a = first term in the series

r = common ratio

S = sum of the series

In this case,

a = 1/7

r = 2/7

S = ?

S = 1/7 / (1 - 2/7) = 9/48

**Therefore, the sum of the infinite series is 9/48.**

Guest Jun 16, 2023