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# (Solved): e Definition. A sequence {a_(n)} is increasing if a_(n)<=a_(n+1) for all n. {a_(n)} is decreasin ...

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Definition. A sequence

`{a_(n)}`

is increasing if

`a_(n)<=a_(n+1)`

for all

`n`

.

`{a_(n)}`

is decreasing if

`a_(n)>=a_(n+1)`

for all

`n`

.

`{a_(n)}`

is monotonic if it is either increasing or decreasing. 3. Classify the sequences in Problem 1 and the geometric sequence

`a_(n)=(-1)^(n)`

as increasing, decreasing, or neither. 4. If a sequence

`{a_(n)}`

converges, does it have to be bounde.. Explain your answer. 5. If a sequence

`{a_(n)}`

is bounded, does it have to converge? Explain your answer. 6. If a sequence

`{a_(n)}`

is bounded and monotonic, does it have to converge? Explain your answer. Monotonic sequence is either increasing or decreasing. If it's bounded, it has a Finite limit. If it's increasing and bounded, it converges to its supremum. If it's decreasing and bounded it converges to its Infimum. In both cases the sequence converges to its limit

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.

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