# Answer to Question #2108 in Real Analysis for Vijay

Question #2108

Prove that if the sequence (Un) is convergent and bounded above by M, then the limit is bounded above by M

Expert's answer

If the sequence is convergent and the limit exists, there exist such N,& that the value of& U(n) ( n > N) tends to limit. Since the sequence is bounded by M, each term |Un| of this sequence is less than M, so the limit cannot be more than M.

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