Does the Alternating Series Test Prove Convergence for Ʃ((-1)^n)*(n+1)/5^n?

[gavin25]

Homework Statement

Show that the series Ʃ 1 to ∞ ((-1)^n)*(n+1)/5^n converges using the alternating series test.

Homework Equations

The Attempt at a Solution

I don't know how to show the series is decreasing. I took the derivative of the function, but it got messy and I don't feel that was the correct way to go. Any help appreciated, thanks.

 

[LCKurtz]

Have you played with the inequality you get when you write $a_{n+1}\le a_n$? Show us what you get...