Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

sam30317

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

  • one year ago
  • one year ago

  • This Question is Closed
  1. sam30317
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\sum_{n=0}^{\inf} \frac{n+3^n}{4^n}\]

    • one year ago
  2. Thomas9
    Best Response
    You've already chosen the best response.
    Medals 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
  3. sam30317
    Best Response
    You've already chosen the best response.
    Medals 0

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

    • one year ago
  4. Thomas9
    Best Response
    You've already chosen the best response.
    Medals 1

    only the 4 is raised to the power n.

    • one year ago
  5. sam30317
    Best Response
    You've already chosen the best response.
    Medals 0

    Nope, so is the 3.

    • one year ago
  6. Thomas9
    Best Response
    You've already chosen the best response.
    Medals 1

    in the first part I mean.

    • one year ago
  7. Thomas9
    Best Response
    You've already chosen the best response.
    Medals 1

    So you don't get n/4 when you do the root test.

    • one year ago
  8. sam30317
    Best Response
    You've already chosen the best response.
    Medals 0

    Then what do i get??

    • one year ago
  9. Thomas9
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\frac{\sqrt[n]{n}}{4}\]

    • one year ago
  10. sam30317
    Best Response
    You've already chosen the best response.
    Medals 0

    lol, that looks more complicated. How would i solve that??

    • one year ago
  11. Thomas9
    Best Response
    You've already chosen the best response.
    Medals 1

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

    • one year ago
  12. Thomas9
    Best Response
    You've already chosen the best response.
    Medals 1

    So \[\frac{\sqrt[n]{n}}{4} \rightarrow \frac{1}{4}\] So that part does converge.

    • one year ago
  13. sam30317
    Best Response
    You've already chosen the best response.
    Medals 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
  14. Thomas9
    Best Response
    You've already chosen the best response.
    Medals 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
  15. Thomas9
    Best Response
    You've already chosen the best response.
    Medals 1

    I do know the n term test actually, thanks wiki.

    • one year ago
  16. sam30317
    Best Response
    You've already chosen the best response.
    Medals 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
  17. Thomas9
    Best Response
    You've already chosen the best response.
    Medals 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
  18. Thomas9
    Best Response
    You've already chosen the best response.
    Medals 1

    It's the first one to try, because it's easy to calculate.

    • one year ago
  19. sam30317
    Best Response
    You've already chosen the best response.
    Medals 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
  20. Thomas9
    Best Response
    You've already chosen the best response.
    Medals 1

    general rule: if you see powers of n: use the ratio test, if you see factorials: ratio test.

    • one year ago
  21. Thomas9
    Best Response
    You've already chosen the best response.
    Medals 1

    Anyway, good luck.

    • one year ago
  22. sam30317
    Best Response
    You've already chosen the best response.
    Medals 0

    thaaanks!!

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.