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INSTRUCTORSCarleen EatonGrant Fraser
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For more information, please see full course syllabus of Algebra 2
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Lecture Comments (1)

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Post by Taylor Wright on July 10, 2013

There is a WAYYYY easier method for turning repeating decimals into fractions.

First, make x= 0.363636...
therefore 100x= 36.36363636...

Second, subtract 100x from x

   x =  00.3636363636...
-100x =  36.3636363636...
-99x = -36.00    (the decimals cancel out)

Third, divide both sides by -99

x= -36/-99

x= 4/11

Infinite Geometric Series

  • Remember that an infinite geometric series converges only if |r| < 1. If you are given a series to evaluate, first check the value of r. If it does not satisfy this condition, the series does not have a sum.

  • To convert a repeating decimal to a fraction, let r = 10-n , where n = number of digits in the repeating pattern of the decimal. Let a1 = the fraction which contains the pattern written once in the numerator and 10n in the denominator.

Infinite Geometric Series

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • What are Infinite Geometric Series? 0:35
    • Partial Sums of the Infinite Series
    • Example
  • Sum of an Infinite Geometric Series 3:16
    • Convergent Series
    • Example
  • Sigma Notation 5:31
    • Example
  • Repeating Decimals 6:38
    • Example
  • Lecture Example 1 9:33
  • Lecture Example 2 11:20
  • Additional Example 3
  • Additional Example 4