How do we prove that a sequence in increasing and boundede?
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Answer:We call the sequence increasing if an<an+1 for every n
We call the sequence decreasing if an>an+1
for every n
If {an}
is an increasing sequence or {an}
is a decreasing sequence we call it monotonic.
if there exists a number m
such that m≤an for every n we say the sequence is bounded below. The number m
is sometimes called a lower bound for the sequence.
If there exists a number M
such that an≤M for every n we say the sequence is bounded above. The number M
is sometimes called an upper bound for the sequence.
If the sequence is both bounded below and bounded above we call the sequence bounded.
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