It's a question that has a few possible answers. As AMT said, several scientists believe that our universe will eventually end in what is called the Big Crunch, while some believe it is possible that our universe is infinite. You can read more about the big crunch Here
You can take a more restrictive view of this: what is the best cosmological model today ('best' of course is somewhat up to you to decide)? What does it say re 'an end'?
You can also take a more relaxed view: humans have been developing theories re the 'end of the universe' for, what, a few thousand years? How have our answers changed, over that incredibly short period of time? What can you conclude from humans' views of whether the universe will 'end' or not, in terms of whether it will, *truly* end?
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