Is constant sequence monotonic?

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Yes, a constant sequence (a number repeated indefinitely) is inceed monotonic: it is both monotonic non-decreasing, and monotonic non-increasing. Hence, one can require that a sequence be strictly monotonic increasing or strictly monotonic decreasing.

Is every constant sequence monotone?

Yes, every constant sequence is monotone, in fact simultaneously monotone non-decreasing and monotone non-increasing. yes, because constant sequence is both increasing and decreasing sequence. so that it is monotonic.

Is the sequence a n = 3 monotonic?

A sequence where a n ≥ a n + 1 for all n ∈ N is monotonic. So given that the sequence a n = 3 is all the same numbers and is neither increasing or decreasing, is it monotonic? Yes, a constant sequence (a number repeated indefinitely) is inceed monotonic: it is both monotonic non-decreasing, and monotonic non-increasing.

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How do you know if a sequence is convergent or monotonic?

A sequence may increase for half a million terms, then decrease; such a sequence is not monotonic. If {a n } is both a bounded sequence and a monotonic sequence, we know it is convergent. If {a n } is convergent, though, it may or may not be monotonic.

Why can’t a monotonic function have more than one constant?

Since a monotonic function has some values that are constant in its domain, this means that there would be more than one value in the range that maps to this constant value.


Monotonic Sequences and Bounded Sequences – Calculus 2


More about Is constant sequence monotonic?


1. Monotonic Sequence, Series (Monotone): Definition

Nov 13, 2020 · A monotonic (monotone) sequence or monotone series, is always either steadily increasing or steadily decreasing. More formally, a series {a n } is monotonic if either: a i + 1 ≥ 1 for every i ≥ 1. a i + 1 ≤ 1 for every i ≥ 1. If the first is true, the series is monotonically increasing. If the second is true, it is monotonically decreasing.

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2. Constant Sequence, Eventually Constant – Calculus How To

Apr 04, 2021 · The constant sequence is a special case of the eventually constant sequence, where a natural number N exists, so that if n ≥ N then a n = a N. In other words, somewhere along the line, the sequence will converge on a natural number. For example, the sequence {1, 2, 3, 4, 4, 4, 4, 4, …} is eventually constant. Constant Sequence Rule. The constant sequence rule …

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4. Monotonous sequences – sangakoo.com

A constant sequence has the form a n = c where c is any number. Any constant sequence has this form. This classification must not be taken as generic since any given sequence is not always increasing or decreasing. If a sequence is increasing or decreasing we will say that it …

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5. Monotonic sequences – Sequences and Series

Feb 25, 2018 · Definition. A sequence is called a monotonic sequence if it is increasing, strictly increasing, decreasing, or strictly decreasing, Examples. The following are all monotonic sequences: The sequence (as it is strictly increasing). The sequence (as it is increasing — and decreasing!). The sequence (as it is decreasing).

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6. Monotonic Sequences – Bridgewater State University

Prove that the sequence which is defined recursively by \begin{align*} s_1 = 1 \amp\amp s_{n+1}=\sqrt{1+s_n} \end{align*} converges. Proof: The sequence is monotonic: If this is indeed true, then all its terms will follow the pattern suggested by its first two, namely that \begin{align*} s_1 = 1 \amp \amp \lt \amp \amp \sqrt{2} = s_2. \end{align*}

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7. How can a constant function be called monotonic? Also, is it

A constant function can’t be strictly monotonic, but just “monotonic” isn’t so fussy. A function is both monotonically increasing and monotonically decreasing over any …

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9. calculus – Determine if the following sequence is monotonic …

Sep 15, 2019 · We now note the the denominator is always positive (as sum of two square roots), so the sign of x n − x n + 1 will be determined by the numerator: 2 x n − 1 − 2 x n, but using our IH we know it’s positive so x n − x n + 1 > 0, and we proved by induction that the sequence is monotonically decreasing.

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