Homework Help: Infinite series

1. Apr 1, 2009

XJellieBX

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

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

I'm not sure if I did it right or where to go from here.

2. Apr 1, 2009

lanedance

hi XjellieBX
do you know how to test for divergence or convergence?

3. Apr 1, 2009

XJellieBX

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. Apr 1, 2009

ascapoccia

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. Apr 1, 2009

XJellieBX

yes. i tried to compare it to the geometric series, but i was having some problems with the denominator

6. Apr 1, 2009

lanedance

i think the ratio test would work well here

7. Apr 1, 2009

kof9595995

comparison test is ok, hint: 5^k+6^k<2*6^k

8. Apr 1, 2009

rwisz

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