So the definition of a bounded sequence is this:(adsbygoogle = window.adsbygoogle || []).push({});

A sequence ##(x_{n})## of real numbers is bounded if there exists a real number ##M>0## such that ##|x_{n}|\le M## for each ##n##

My question is pretty simple. How does one choose the M, based on the sequence in order to arrive at the conclusion? This has been something I've been confused about for a number of years and it seems like it all depends on the sequence in question. But is there a general rule that applies in these cases?

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# I For direct proof, how do you choose M for bounded sequence?

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