Answer:
0.25 Converges
Step-by-step explanation:
First, we need to expand our series so that we get the following:
[tex]\sum _{n=1}^{\infty \:}\frac{n}{4^n}+\frac{1}{4^{n+1}}[/tex]
We can then use the series ratio test on each term. (L < 1 = absolutely convergent)
[tex]\sum _{n=1}^{\infty \:}\frac{n}{4^n}[/tex]
[tex]\lim_{n \to \infty} \frac{n}{4^{n}\\}[/tex] =
⇒ converges
[tex]\sum _{n=1}^{\infty \:}\frac{1}{4^n^+1}[/tex]
[tex]\lim_{n \to \infty} \frac{n}{4^{n}^+1\\}[/tex]
⇒ converges
converges + converges
= converges
~Hope this helps! Once again, sorry if my explanation is a bit confusing~
