If a sequence is bounded and monotonic then it is convergent, Mathematics

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Theorem

If {a_n} is bounded and monotonic then { a_n} is convergent.

Be cautious to not misuse this theorem. It does not state that if a sequence is not bounded and/or not monotonic that it is divergent. The sequence in that instance was not monotonic but it does converge.

Note: that we can make various variants of this theorem. If {a_n}is bounded above and increasing after that it converges and similarly if {a_n} n a is bounded below and decreasing after that it converges.

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