Here' we're asked to determine whether the sequence converges or diverges, and if it converges we are asked to find the limit. We are given the sequence

So I can see by putting this into my calculator that this is going to converge to 8. My problem is showing this mathematically. Here's where I'm stuck.

Easy enough, now the tough part....

Where do I even begin on this? Do I need to use a natural log or something? Wood that be the thing to do? (terrible pun, but I had to do it.)

I obviously can't say that my exponent is going to 0 as n goes to infinity, because that's just not true. If it were the answer would just be 1 and that'd be it, but that's obviously not the case.

If anyone could help point me in the right direction, that'd just be super.

Thanks!