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## Chapter 4 Series and Approximations

### 4.1 Sequences, Progressions, and Series

• This section includes sequences, arithmetic, and geometric progressions, and arithmetic and geometric series.

• A sequence is a set of numbers called terms, which are arranged in a succession in which there is a relationship or rule between each successive number. A sequence can be finite or infinite. A finite sequence has a last term and an infinite sequence has no last term.

• The following is an example of a finite sequence:

{3, 6, 9, 12, 15, 18}

In this sequence each number has a value of 3 more than the preceding number.

• The following is an example of an infinite sequence describing the function f(x) = 1/x:

{1/1, 1/2, 1/3, 1/4, 1/5, 1/6,…}

where the domain set ...

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