(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If {c_{n}} is a convergent sequence of real numbers, does there necessarily exist R> 0 such that |c_{n}|≤ R for every n ∈ N? Equivalently, is {c_{n}: n ∈ N} a bounded set of real numbers? Explain why or why not.

2. Relevant equations

n/a

3. The attempt at a solution

I would think this is patently obvious given the definition of convergence but I don't really know how to put the proof in words and numbers.

c_{n}approaches some value c for large n but it can do so in a number of ways so how can i prove that there is always some R that is larger or equal to all elements c_{n}?

Thanks for the help!

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# Homework Help: Convergence of sequences

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