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- anonymous

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

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- anonymous

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

- katieb

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- anonymous

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

- anonymous

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

- anonymous

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

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- anonymous

only the 4 is raised to the power n.

- anonymous

Nope, so is the 3.

- anonymous

in the first part I mean.

- anonymous

So you don't get n/4 when you do the root test.

- anonymous

Then what do i get??

- anonymous

\[\frac{\sqrt[n]{n}}{4}\]

- anonymous

lol, that looks more complicated. How would i solve that??

- anonymous

Well, \[lim_{n \rightarrow \infty} \sqrt[n]{n} =1\]
It's standard thing, good idea to remember that limit.

- anonymous

So \[\frac{\sqrt[n]{n}}{4} \rightarrow \frac{1}{4}\]
So that part does converge.

- anonymous

Oooo kaaay, lol. Thanks!! Im having a hard time remembering when all the tests conv or diverge. Like with n term test: if it equals 0, its inconclusive. And p series: p>1, conv.
How did u manage to memorize them w/o confusing yourself??

- anonymous

I only know the ratio and the root test, not sure what n term test or p series is.
For ratio and root test it's the same, <1 to converge, 1 inconlusive, so that's not too hard to remember.

- anonymous

I do know the n term test actually, thanks wiki.

- anonymous

Lol. I had a test on this stuff already and it was crazy how confused I got (i.e I failed it). Now my final is today and im going crazy, lol

- anonymous

Well the term test makes a lot of sense, if the limit doesn't equal zero, you're adding an infinite amount of numbers that aren't close to zero, so that's sure to diverge.

- anonymous

It's the first one to try, because it's easy to calculate.

- anonymous

Pseries, nth term, geom are easy to remember. I know about the root/ration , thanks to you! Now....on to others

- anonymous

general rule: if you see powers of n: use the ratio test,
if you see factorials: ratio test.

- anonymous

Anyway, good luck.

- anonymous

thaaanks!!

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