# 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...