Question

How do we prove that a sequence in increasing and boundede?

Answer 1

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.