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