# Infinite series

## Homework Statement

$$\sum\frac{7^{k}}{5^{k}+6^{k}}$$
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.

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

we learned the root test, the ratio test, and the basic comparison test in class. but i'm not sure which one to use.

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)?

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

lanedance
Homework Helper
i think the ratio test would work well here

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

i think the ratio test would work well here

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