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Determine whether the sequence is bounded, bounded below, bounded above, or none of the above....

Question:

Determine whether the sequence is bounded, bounded below, bounded above, or none of the above. Show your work and reasonings.

{eq}{a_n} = {(-1)^n \frac {3n- 1}{n}} {/eq}

Bounded Sequence:

A sequence {eq}\{a_n \} {/eq} is said to be bounded below if there exists {eq}m\in \mathbb{R} {/eq} such that {eq}m \leq a_n \ \ \forall \ n . {/eq}

A sequence {eq}\{a_n \} {/eq} is said to be bounded above if there exists {eq}M\in \mathbb{R} {/eq} such that {eq}a_n \leq M \ \ \forall \ n . {/eq}

A sequence {eq}\{a_n \} {/eq} is said to be bounded if there exists {eq}K \in \mathbb{R} {/eq} such that {eq}| a_n |\leq K \ \ \forall \ n . {/eq}

Answer and Explanation: 1

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Given sequence is:

{eq}{a_n} = {(-1)^n \frac {3n- 1}{n}} . {/eq}

Now,

{eq}\begin{align} | a_n | = | (-1)^n \frac {3n- 1}{n} | &= \frac {3n-...

See full answer below.


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Special Sequences and How They Are Generated

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Chapter 21 / Lesson 17
11K

Special sequences are a string of numbers that have a unique pattern to them. Discover how special sequences are generated and some types such as triangular, tetrahedral, cube, square, and fibonacci sequences.


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