Does the series converge or diverge? Summation (n+3^n)/4^n n=0 to inf.

Does the series converge or diverge? Summation (n+3^n)/4^n n=0 to inf.

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\[\sum_{n=0}^{\inf} \frac{n+3^n}{4^n}\]

I would seperate it in two parts: n/4^n+(3/4)^n
Then I'd try the root test on both parts seperately.

So i would be left with (n/4) = infinity= div
(3/4) <1 = conv..
Because one div, they both dierge???

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