anonymous
  • anonymous
Does the series converge or diverge? Summation (n+3^n)/4^n n=0 to inf.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\sum_{n=0}^{\inf} \frac{n+3^n}{4^n}\]
anonymous
  • 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
  • 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
  • anonymous
only the 4 is raised to the power n.
anonymous
  • anonymous
Nope, so is the 3.
anonymous
  • anonymous
in the first part I mean.
anonymous
  • anonymous
So you don't get n/4 when you do the root test.
anonymous
  • anonymous
Then what do i get??
anonymous
  • anonymous
\[\frac{\sqrt[n]{n}}{4}\]
anonymous
  • anonymous
lol, that looks more complicated. How would i solve that??
anonymous
  • anonymous
Well, \[lim_{n \rightarrow \infty} \sqrt[n]{n} =1\] It's standard thing, good idea to remember that limit.
anonymous
  • anonymous
So \[\frac{\sqrt[n]{n}}{4} \rightarrow \frac{1}{4}\] So that part does converge.
anonymous
  • 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
  • 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
  • anonymous
I do know the n term test actually, thanks wiki.
anonymous
  • 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
  • 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
  • anonymous
It's the first one to try, because it's easy to calculate.
anonymous
  • anonymous
Pseries, nth term, geom are easy to remember. I know about the root/ration , thanks to you! Now....on to others
anonymous
  • anonymous
general rule: if you see powers of n: use the ratio test, if you see factorials: ratio test.
anonymous
  • anonymous
Anyway, good luck.
anonymous
  • anonymous
thaaanks!!

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