1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Infinite series

  1. Apr 1, 2009 #1
    1. The problem statement, all variables and given/known data
    [tex]\sum\frac{7^{k}}{5^{k}+6^{k}}[/tex]
    Determine if this infinite series (from k=0 to infinity) converges or diverges.


    2. The attempt at a solution
    I set ak=[tex]\frac{7^{k}}{5^{k}+6^{k}}[/tex]
    then I took the Ln of both sides
    ln ak=ln[tex]\frac{7^{k}}{5^{k}+6^{k}}[/tex]=ln7k-ln(5k+6k)

    I'm not sure if I did it right or where to go from here.
     
  2. jcsd
  3. Apr 1, 2009 #2

    lanedance

    User Avatar
    Homework Helper

    hi XjellieBX
    do you know how to test for divergence or convergence?
     
  4. Apr 1, 2009 #3
    we learned the root test, the ratio test, and the basic comparison test in class. but i'm not sure which one to use.
     
  5. Apr 1, 2009 #4
    no need to take the natural log; that is making your life too hard. have you tried to look at a comparison test with a special type of series (geometric, p-series, harminic, alternating, etc)?
     
  6. Apr 1, 2009 #5
    yes. i tried to compare it to the geometric series, but i was having some problems with the denominator
     
  7. Apr 1, 2009 #6

    lanedance

    User Avatar
    Homework Helper

    i think the ratio test would work well here
     
  8. Apr 1, 2009 #7
    comparison test is ok, hint: 5^k+6^k<2*6^k
     
  9. Apr 1, 2009 #8
    most definitely. notice how all terms have the same exponent...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Infinite series
  1. Infinite series (Replies: 3)

  2. Infinite series (Replies: 4)

  3. Infinite Series (Replies: 2)

  4. Infinite series. (Replies: 4)

  5. Infinite series. (Replies: 1)

Loading...