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

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

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

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

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

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

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

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

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

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

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

sam30317
 2 years ago
Best ResponseYou've already chosen the best response.0Oooo 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??

Thomas9
 2 years ago
Best ResponseYou've already chosen the best response.1I 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.

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

sam30317
 2 years ago
Best ResponseYou've already chosen the best response.0Lol. 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

Thomas9
 2 years ago
Best ResponseYou've already chosen the best response.1Well 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.

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

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

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