# Series, Convergence, Divergence

## Sequences

Definition, with examples of convergent and divergent sequences.

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## Tests for Convergence/Divergence of Sequences

The squeezing lemma and the monotone convergence test for sequences.

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## Series

Definition, using the sequence of partial sums and the sequence of partial absolute sums. Absolutely convergent and conditionally convergent series are defined, with examples of the harmonic and alternating harmonic series.

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## Introduction to Infinite Series

Definitions of sequences and series, with examples of harmonic, geometric, and exponential series as well as a definition of convergence.

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## Manipulating Absolutely Convergent Series

Examples of the uses of manipulating or rearranging the terms of an absolutely convergent series.

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## Computing Series Partial Sums

Steps for using a spreadsheet to compute the partial sums of a series.

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## Infinite Series

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Determining whether a given series converges or diverges.

Three questions which involve finding the sum of a geometric series, writing infinite decimals as the quotient of integers, determining whether fifteen different series converge or diverge, and using Riemann sums to show a bound on the series of sums of 1/n.

## Basic Definition of Infinite Series

Five questions which involve finding whether a series converges or diverges, finding the sum of a series, finding a rational expression for an infinite decimal, and finding the total distance traveled by a ball as it bounces up and down repeatedly.

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