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sam30317

  • 2 years ago

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

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  1. sam30317
    • 2 years ago
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    \[\sum_{n=0}^{\inf} \frac{n+3^n}{4^n}\]

  2. Thomas9
    • 2 years ago
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    I would seperate it in two parts: n/4^n+(3/4)^n Then I'd try the root test on both parts seperately.

  3. sam30317
    • 2 years ago
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    So i would be left with (n/4) = infinity= div (3/4) <1 = conv.. Because one div, they both dierge???

  4. Thomas9
    • 2 years ago
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    only the 4 is raised to the power n.

  5. sam30317
    • 2 years ago
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    Nope, so is the 3.

  6. Thomas9
    • 2 years ago
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    in the first part I mean.

  7. Thomas9
    • 2 years ago
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    So you don't get n/4 when you do the root test.

  8. sam30317
    • 2 years ago
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    Then what do i get??

  9. Thomas9
    • 2 years ago
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    \[\frac{\sqrt[n]{n}}{4}\]

  10. sam30317
    • 2 years ago
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    lol, that looks more complicated. How would i solve that??

  11. Thomas9
    • 2 years ago
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    Well, \[lim_{n \rightarrow \infty} \sqrt[n]{n} =1\] It's standard thing, good idea to remember that limit.

  12. Thomas9
    • 2 years ago
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    So \[\frac{\sqrt[n]{n}}{4} \rightarrow \frac{1}{4}\] So that part does converge.

  13. sam30317
    • 2 years ago
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    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??

  14. Thomas9
    • 2 years ago
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    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.

  15. Thomas9
    • 2 years ago
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    I do know the n term test actually, thanks wiki.

  16. sam30317
    • 2 years ago
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    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

  17. Thomas9
    • 2 years ago
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    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.

  18. Thomas9
    • 2 years ago
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    It's the first one to try, because it's easy to calculate.

  19. sam30317
    • 2 years ago
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    Pseries, nth term, geom are easy to remember. I know about the root/ration , thanks to you! Now....on to others

  20. Thomas9
    • 2 years ago
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    general rule: if you see powers of n: use the ratio test, if you see factorials: ratio test.

  21. Thomas9
    • 2 years ago
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    Anyway, good luck.

  22. sam30317
    • 2 years ago
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    thaaanks!!

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