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sam30317
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Does the series converge or diverge? Summation (n+3^n)/4^n n=0 to inf.
 2 years ago
 2 years ago
sam30317 Group Title
Does the series converge or diverge? Summation (n+3^n)/4^n n=0 to inf.
 2 years ago
 2 years ago

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sam30317 Group TitleBest ResponseYou've already chosen the best response.0
\[\sum_{n=0}^{\inf} \frac{n+3^n}{4^n}\]
 2 years ago

Thomas9 Group TitleBest ResponseYou've already chosen the best response.1
I would seperate it in two parts: n/4^n+(3/4)^n Then I'd try the root test on both parts seperately.
 2 years ago

sam30317 Group TitleBest ResponseYou've already chosen the best response.0
So i would be left with (n/4) = infinity= div (3/4) <1 = conv.. Because one div, they both dierge???
 2 years ago

Thomas9 Group TitleBest ResponseYou've already chosen the best response.1
only the 4 is raised to the power n.
 2 years ago

sam30317 Group TitleBest ResponseYou've already chosen the best response.0
Nope, so is the 3.
 2 years ago

Thomas9 Group TitleBest ResponseYou've already chosen the best response.1
in the first part I mean.
 2 years ago

Thomas9 Group TitleBest ResponseYou've already chosen the best response.1
So you don't get n/4 when you do the root test.
 2 years ago

sam30317 Group TitleBest ResponseYou've already chosen the best response.0
Then what do i get??
 2 years ago

Thomas9 Group TitleBest ResponseYou've already chosen the best response.1
\[\frac{\sqrt[n]{n}}{4}\]
 2 years ago

sam30317 Group TitleBest ResponseYou've already chosen the best response.0
lol, that looks more complicated. How would i solve that??
 2 years ago

Thomas9 Group TitleBest ResponseYou've already chosen the best response.1
Well, \[lim_{n \rightarrow \infty} \sqrt[n]{n} =1\] It's standard thing, good idea to remember that limit.
 2 years ago

Thomas9 Group TitleBest ResponseYou've already chosen the best response.1
So \[\frac{\sqrt[n]{n}}{4} \rightarrow \frac{1}{4}\] So that part does converge.
 2 years ago

sam30317 Group TitleBest ResponseYou've already chosen the best response.0
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??
 2 years ago

Thomas9 Group TitleBest ResponseYou've already chosen the best response.1
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.
 2 years ago

Thomas9 Group TitleBest ResponseYou've already chosen the best response.1
I do know the n term test actually, thanks wiki.
 2 years ago

sam30317 Group TitleBest ResponseYou've already chosen the best response.0
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
 2 years ago

Thomas9 Group TitleBest ResponseYou've already chosen the best response.1
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.
 2 years ago

Thomas9 Group TitleBest ResponseYou've already chosen the best response.1
It's the first one to try, because it's easy to calculate.
 2 years ago

sam30317 Group TitleBest ResponseYou've already chosen the best response.0
Pseries, nth term, geom are easy to remember. I know about the root/ration , thanks to you! Now....on to others
 2 years ago

Thomas9 Group TitleBest ResponseYou've already chosen the best response.1
general rule: if you see powers of n: use the ratio test, if you see factorials: ratio test.
 2 years ago

Thomas9 Group TitleBest ResponseYou've already chosen the best response.1
Anyway, good luck.
 2 years ago

sam30317 Group TitleBest ResponseYou've already chosen the best response.0
thaaanks!!
 2 years ago
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