Compute the limit (exponents with variable)

[PirateFan308]

Homework Statement

Compute the limits of the following sequence (show your work):

3ⁿ⁺¹7ⁿ⁺³
4ⁿ5^n-2

(sorry if it looks funny ... the top line is divided by the bottom line)

The Attempt at a Solution

I was thinking that I should get the exponents the same and add/subtract the exponents, but I don't remember how to, or if this is even possible.

 

[PirateFan308]

I think I figured out a bit more. I have learned that I can split up the limit, so it will look like:
(lim3ⁿ⁺¹)(lim7ⁿ⁺³) ÷ (lim4ⁿ)(lim5^n-2)

and each of these individual limits equals +∞.

So I have +∞ ÷ +∞. Does this still equal infinity, 0, or does not exist?

 

[Dick]

I think I figured out a bit more. I have learned that I can split up the limit, so it will look like:
(lim3ⁿ⁺¹)(lim7ⁿ⁺³) ÷ (lim4ⁿ)(lim5^n-2)

and each of these individual limits equals +∞.

So I have +∞ ÷ +∞. Does this still equal infinity, 0, or does not exist?

Try this. 2^n/3^n=(2/3)^n. What's the limit of that? How about 3^n/2^n? There's a reason why infinity/infinity is called 'indeterminant'.