1.6A: Geometric Infinite Series

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Presentation transcript:

1.6A: Geometric Infinite Series Worksheet Key 12/2/2018 10:27 PM 1.6A: Geometric Infinite Series

Geometric Infinite Series Section 12.5 Pre–Calculus, Revised ©2015 12/2/2018 10:27 PM 1.6A: Geometric Infinite Series

1.6A: Geometric Infinite Series Definitions Infinite Geometric Series has unlimited terms Limit is where the numbers of an infinite sequence or series approaches as the term number increases Convergent series is where absolute value of ratio is less than 1; it DOES have an infinite sum Divergent series is where absolute value of ratio is more than 1; it DOES NOT have an infinite sum Formula: 𝐒= 𝒂 𝟏 𝟏−𝒓 12/2/2018 10:27 PM 1.6A: Geometric Infinite Series

Convergent vs Divergent Formula: 𝐒= 𝒂 𝟏 𝟏−𝒓 Determine whether these series is either convergent or divergent. Find the ratio to identify whether it is convergent or divergent. Ratio: 16/32 = 1/2 Ratio: 4/2 = 2 Divergent Convergent 12/2/2018 10:27 PM 1.6A: Geometric Infinite Series

1.6A: Geometric Infinite Series Example 1 Given 32 + 16 + 8 + 4 + 2 + 1 + … and find the sum of the infinite geometric series, if it exists. Then, identify whether it converges or diverges 12/2/2018 10:27 PM 1.6A: Geometric Infinite Series

1.6A: Geometric Infinite Series Example 2 Given 5 + 4 + 3.2 + 2.56 + …. Find the sum of the infinite geometric series, if it exists. 12/2/2018 10:27 PM 1.6A: Geometric Infinite Series

1.6A: Geometric Infinite Series Example 3 Given 8 + 12 + 18 + 27 + …. Find the sum of the infinite geometric series, if it exists. 12/2/2018 10:27 PM 1.6A: Geometric Infinite Series

1.6A: Geometric Infinite Series Your Turn Given 2 + 4/3 + 8/9 + …. Find the sum of the infinite geometric series, if it exists. 12/2/2018 10:27 PM 1.6A: Geometric Infinite Series

1.6A: Geometric Infinite Series Example 4 Evaluate 𝒌=𝟏 ∞ −𝟓 𝟒 𝟓 𝒌 12/2/2018 10:27 PM 1.6A: Geometric Infinite Series

1.6A: Geometric Infinite Series Your Turn Evaluate 𝒌=𝟏 ∞ 𝟏 𝟐 𝒌 12/2/2018 10:27 PM 1.6A: Geometric Infinite Series

1.6A: Geometric Infinite Series Assignment Worksheet 12/2/2018 10:27 PM 1.6A: Geometric Infinite Series