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Chapter 9

Chapter 9 . Sequences and Series. 9.1 – Sequences and Series. Sequence: function whose domain is the set of positive integers…. i.o.w. its ordered so that is has a first term, second term, etc. Infinite sequence – domain is the set of positive integers (continues infinitely )

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Chapter 9

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  1. Chapter 9 Sequences and Series

  2. 9.1 – Sequences and Series • Sequence: function whose domain is the set of positive integers…. i.o.w. its ordered so that is has a first term, second term, etc. • Infinite sequence – domain is the set of positive integers (continues infinitely) • Finite sequence - domain consists of “n” positive integers (it has an end)

  3. Finding terms of a sequence: • an=(-1) n+1 2n - 1

  4. Finding “nth” terms… writing equations to model sequences • 1, 3, 5, 7, …. • 3, 7, 11, 15, 19, …. • 2, -4, 6, -8, 10, ….

  5. Some more practice modeling sequences… • 2, 5, 10, 17, … • 2, -5, 10, -17, … • 2, 3/2, 4/3, 5/4, … • A few more…. Pg. 621 #’s 46-50 even

  6. Recursive formulas… • To be a recursive formula, the first term must be given and the remaining terms are defined using the previous term • Best known recursive formula is the Fibonacci Sequence… look on page 616 example 4 • An example… Write the first five terms for: a1=15 an+1 = an + 3

  7. Factorial Notation…. ! • n factorial is defined as: n! = 1•2•3•4 ••• (n-1)•n Examples: 2! = 10! = 2n! =

  8. Find the first 4 terms… • an=2n n!

  9. Evaluating factorials without a calculator… • 1) 8! 3) n! 2! •6! (n-1)! • 2) 2!•6! 4) (n+2)! 3!•5! n!

  10. Summation Notation… finding the sum of a sequence i: index of summation n: upper limit of summation 1: lower limit of summation

  11. Finding finite sums… 1) 2)

  12. Properties of Sums.. • Please look at chart on page 619 • Also notice Sum for INFINITE SEQUENCE – page 619 • *We will not focus on this because if you remember there are formulas to solve!!

  13. Section 9.1 – HW • Day 2

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