Infinite Sum

Question

-1

300

2

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

Guest Dec 3, 2021

geno3141 · Answer 1 · 2021-12-04T12:07:49

1) Divide this into two infinite geometric series:

1/7 + 1/7³ + 1/7⁵ + ...

and

2/7² + 2/7⁴ + 2/7⁶ + ...

2) Find the sum of each part, using this formula: Sum = a / (1 - r)

3) Add the two sums together to find the final result.