Given the following sequences. Determine for each sequence it it converges. If so, find its...

Question:

Given the following sequences. Determine for each sequence it it converges. If so, find its limit. Assume for all sequences {eq}n \geq 1 {/eq} If it diverges, explain.

1) {eq}a_n = \frac {1-2n}{1+2n} {/eq}

2) {eq}a_n = \frac {n^2 - 2n+1}{n+1)} {/eq}

3) {eq}a_n = \frac {(-1)^n}{2n-1} {/eq}

5) {eq}a_n = \sqrt [n] {3} {/eq}

Sequence Divergence and Convergence:

Let {eq}\left\{ {{l_n}} \right\} {/eq} be the sequence, then

If the sequence has a finite limit then it is said to be convergent and if the sequence has an infinite or does not exist, the sequence is said to be divergent.

Answer and Explanation: 1

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{eq}\displaystyle \eqalign{ & 1) \cr & {a_n} = \frac{{1 - 2n}}{{1 + 2n}} \cr & \mathop {\lim }\limits_{n \to \infty } {a_n} = \mathop {\lim...

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Special Sequences and How They Are Generated

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Chapter 21 / Lesson 17
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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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