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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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  1. sam30317 Group Title
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    \[\sum_{n=0}^{\inf} \frac{n+3^n}{4^n}\]

    • 2 years ago
  2. Thomas9 Group Title
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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.

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

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

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

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

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

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

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

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

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

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

    • 2 years ago
  13. sam30317 Group Title
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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??

    • 2 years ago
  14. Thomas9 Group Title
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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.

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

    • 2 years ago
  16. sam30317 Group Title
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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

    • 2 years ago
  17. Thomas9 Group Title
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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.

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

    • 2 years ago
  19. sam30317 Group Title
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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

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

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

    • 2 years ago
  22. sam30317 Group Title
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    thaaanks!!

    • 2 years ago
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