# Finding the limit of a sequence a quotient of two power functions

1. Mar 25, 2013

### Aerospace93

1. The problem statement, all variables and given/known data
lim x-> infinity 3n+2/5n

2. Mar 25, 2013

### Staff: Mentor

I think you missed part 3 of the homework template: What did you do so far?
There is a nice way to simplify the expression.

3. Mar 25, 2013

### Aerospace93

can it be simplified to 5^n-2 (3/5)^n+2

4. Mar 25, 2013

### Staff: Mentor

If you add some brackets, right. There is an easier way to write it, but this one is fine as well.
You should be able to see the limit of that expression.

5. Mar 25, 2013

### Aerospace93

1/3^2 * (3/5)^n. the geometric series will be convergent since |r|=3/5<1?

6. Mar 25, 2013

### Staff: Mentor

3^2, not 1/3^2

Right.

7. Mar 25, 2013

### jbunniii

It's not a geometric series, is it? The problem statement indicates a sequence, not a series. The conclusion is correct, though: $(3/5)^n \rightarrow 0$ because $|3/5| < 1$. (Do you know how to prove that?)