Infinite Geometric
      Series




      iphone to infinity for
      righty's by flickr user KIT
Given a geometric sequence in which   and   , what is the
value of ?
Series: The sum of numbers in a sequence to a particular term in a
sequence.

  Example:     denotes the sum of the first 5...
Sigma Notation: A shorthand way to write a series.
Example:
         4
        ∑(2n - 3) means (2(1) -3) + (2(2) -3) + (2(...
Series: The sum of numbers in a sequence to a particular term in a
sequence.

  Example:     denotes the sum of the first 5...
or
Given the geometric sequence in which   and r = , which
term has a value of 27?




Find the sum of the first 5 terms.
Given the geometric sequence in which   and r = , which
term has a value of 27?




Find the sum of the first 5 terms.
Infinite Geometric
      Series




      iphone to infinity for
      righty's by flickr user KIT
Infinite Geometric Series




 Why is that the formula?
CONVERGENT SERIES
     0 < |r| <1


DIVERGENT SERIES
      |r| > 1
Find the infinite sum for a geometric series given:   a = 12   r= 2
                                                       ...
Pre-Cal 40S June 5, 2009
Pre-Cal 40S June 5, 2009
Pre-Cal 40S June 5, 2009
Upcoming SlideShare
Loading in...5
×

Pre-Cal 40S June 5, 2009

1,554

Published on

Infinite geometric sequences.

Published in: Education, Technology, Business
0 Comments
1 Like
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total Views
1,554
On Slideshare
0
From Embeds
0
Number of Embeds
15
Actions
Shares
0
Downloads
8
Comments
0
Likes
1
Embeds 0
No embeds

No notes for slide

Transcript of "Pre-Cal 40S June 5, 2009"

  1. 1. Infinite Geometric Series iphone to infinity for righty's by flickr user KIT
  2. 2. Given a geometric sequence in which and , what is the value of ?
  3. 3. Series: The sum of numbers in a sequence to a particular term in a sequence. Example: denotes the sum of the first 5 terms. denotes the sum of the first n terms. Artithmetic Series: The sum of numbers in an arithmetic sequence given by is the sum to the nth term n is the quot;rankquot; of the nth term a is the first term in the sequence d is the common difference
  4. 4. Sigma Notation: A shorthand way to write a series. Example: 4 ∑(2n - 3) means (2(1) -3) + (2(2) -3) + (2(3) -3) + (2(4) -3) n=1 = -1 + 1 + 3 + 5 =8 Σ is capital sigma (from the greek alphabet); means sum subscript n = 1 means quot;start with n = 1 and evaluate (2n - 3)quot; superscript 4 means keep evaluating (2n - 3) for successive integral values of n; stop when n = 4; then add all the terms (2n - 3) is the implicit definition of the sequence
  5. 5. Series: The sum of numbers in a sequence to a particular term in a sequence. Example: denotes the sum of the first 5 terms. denotes the sum of the first n terms. Geometric Series: The sum of numbers in an geometric sequence given by or is the sum to the nth term n is the quot;rankquot; of the nth term a is the first term in the sequence d is the common difference
  6. 6. or
  7. 7. Given the geometric sequence in which and r = , which term has a value of 27? Find the sum of the first 5 terms.
  8. 8. Given the geometric sequence in which and r = , which term has a value of 27? Find the sum of the first 5 terms.
  9. 9. Infinite Geometric Series iphone to infinity for righty's by flickr user KIT
  10. 10. Infinite Geometric Series Why is that the formula?
  11. 11. CONVERGENT SERIES 0 < |r| <1 DIVERGENT SERIES |r| > 1
  12. 12. Find the infinite sum for a geometric series given: a = 12 r= 2 3

×