SFM Productions Presents: Another action-packet episode of “Adventures inPre-Calculus!” 9.1Sequences and Series.

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Presentation transcript:

SFM Productions Presents: Another action-packet episode of “Adventures inPre-Calculus!” 9.1Sequences and Series

Homework for section 9.1 p647Part 1:19-35, (EOO if too much) Part 2: (EOO if too much)

A sequence is a function whose domain is the set of positive integers Finite Sequence: domain consists of the first n positive integers.

Sometimes can start with a subscript of 0… a 0, a 1, a 2., a 3 … Finding terms of a sequence:

There may be more than one pattern that works, but we are only after the most apparent term… Find the n th term: (that means find the formula, or model…… a n = some formula) n anan

n anan

n anan

n anan

Some sequences are defined recursively, which means you need to be given one or more of the first term(s) - then the following terms can be found using the previous ones. Recursive sequences use: a k Given: Find the next 4 terms…

Given: Find the next 4 terms… We want a 2. And since recursive sequences have the form: a k, that means k = You’re set to do up through problem 59.

Another type of sequence is defined as: ! ! = factorialIf n is an integer, then n! is defined as:

Evaluating factorials: You’re set to do up through problem 83.

Summation Notation:a convenient way to notate the sum of the terms of a finite sequence. Also known as Sigma notation.

Find the sum of the first 6 terms (starting with 1) of the sequence: 3n - 1.

Break out your battery operated brain…

Properties of Sums of sequences:

Infinite series Finite series (also called the nth partial sum)

1. Find the 3 rd partial sum. 2. Find the sum of the whole thing…

1. Find the 3 rd partial sum. 2. Find the sum of the whole thing…

Go! Do!