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Infinite series

  1. Apr 1, 2009 #1
    1. The problem statement, all variables and given/known data
    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


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    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


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    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...
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