Question

Please helpppppp meeee

Answer 1

Answer:

0.25     Converges

Step-by-step explanation:

First, we need to expand our series so that we get the following:

$\sum _{n=1}^{\infty \:}\frac{n}{4^n}+\frac{1}{4^{n+1}}$

We can then use the series ratio test on each term. (L < 1 = absolutely convergent)

$\sum _{n=1}^{\infty \:}\frac{n}{4^n}$

$\lim_{n \to \infty} \frac{n}{4^{n}\\}$ =

⇒  converges

$\sum _{n=1}^{\infty \:}\frac{1}{4^n^+1}$

$\lim_{n \to \infty} \frac{n}{4^{n}^+1\\}$

⇒  converges

converges + converges

= converges

~Hope this helps! Once again, sorry if my explanation is a bit confusing~