How to prove that a limit exists?

Hello.

I have to prove that an actual limit exists while n is approaching infinity.

I do NOT need to get to the exact limit itself.

1. It is easy to understand (and prove), that sequence never decreases. That's already half of the job.

2. I need to make some manipulations that would lead to any specific number being greater than my sequence (irrespective of natural n value).

http://www.ipix.lt/images/91408942.jpg

I get no further than this, a remaining product is a real headache.

Thank you for ideas and sorry for possibly broken English :D