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

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sam30317Best ResponseYou've already chosen the best response.0
\[\sum_{n=0}^{\inf} \frac{n+3^n}{4^n}\]
 one year ago

Thomas9Best 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.
 one year ago

sam30317Best 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???
 one year ago

Thomas9Best ResponseYou've already chosen the best response.1
only the 4 is raised to the power n.
 one year ago

Thomas9Best ResponseYou've already chosen the best response.1
in the first part I mean.
 one year ago

Thomas9Best ResponseYou've already chosen the best response.1
So you don't get n/4 when you do the root test.
 one year ago

Thomas9Best ResponseYou've already chosen the best response.1
\[\frac{\sqrt[n]{n}}{4}\]
 one year ago

sam30317Best ResponseYou've already chosen the best response.0
lol, that looks more complicated. How would i solve that??
 one year ago

Thomas9Best 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.
 one year ago

Thomas9Best ResponseYou've already chosen the best response.1
So \[\frac{\sqrt[n]{n}}{4} \rightarrow \frac{1}{4}\] So that part does converge.
 one year ago

sam30317Best 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??
 one year ago

Thomas9Best 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.
 one year ago

Thomas9Best ResponseYou've already chosen the best response.1
I do know the n term test actually, thanks wiki.
 one year ago

sam30317Best 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
 one year ago

Thomas9Best 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.
 one year ago

Thomas9Best ResponseYou've already chosen the best response.1
It's the first one to try, because it's easy to calculate.
 one year ago

sam30317Best 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
 one year ago

Thomas9Best 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.
 one year ago
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