Infinite series

  • Thread starter XJellieBX
  • Start date
  • #1
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Homework Statement


[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.
 

Answers and Replies

  • #2
lanedance
Homework Helper
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hi XjellieBX
do you know how to test for divergence or convergence?
 
  • #3
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we learned the root test, the ratio test, and the basic comparison test in class. but i'm not sure which one to use.
 
  • #4
21
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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)?
 
  • #5
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yes. i tried to compare it to the geometric series, but i was having some problems with the denominator
 
  • #6
lanedance
Homework Helper
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i think the ratio test would work well here
 
  • #7
679
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comparison test is ok, hint: 5^k+6^k<2*6^k
 
  • #8
45
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i think the ratio test would work well here

most definitely. notice how all terms have the same exponent...
 

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