I finding the sum of this series

[Randall]

Homework Statement

Find the sum of the series from k=0 to infinity of ((4^k)-(3^k))/(5^k)

Homework Equations

I'm not sure exactly. I know the test for divergence is if lim n approaches infinity of the function from m=1 to infinity does not equal 0 then the series cannot diverge

The Attempt at a Solution

see attached but really my work is a lame attempt at a test for divergence, and not so much an attempt at the sum. Please I need help finding the sum.

 

[PeroK]

You're overlooking something very simple. It's difficult to give a hint without giving away the answer. Just think of the simplest thing you can do with the terms.

 

[Randall]

Ahhhh. I see. This is simply the sum of two different geometric series - one with a ratio of 4/5 and one with a ratio of 3/5, yes? I feel silly now