1. 1.6A: Geometric Infinite Series
Worksheet Key
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1.6A: Geometric Infinite Series

2. Geometric Infinite Series
Section 12.5
Pre–Calculus, Revised ©2015
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1.6A: Geometric Infinite Series

3. 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
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1.6A: Geometric Infinite Series

4. 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
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1.6A: Geometric Infinite Series

5. 1.6A: Geometric Infinite Series
Example 1
Given … and find the sum of the infinite geometric series, if it exists. Then, identify whether it converges or diverges
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1.6A: Geometric Infinite Series

6. 1.6A: Geometric Infinite Series
Example 2
Given …. Find the sum of the infinite geometric series, if it exists.
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1.6A: Geometric Infinite Series

7. 1.6A: Geometric Infinite Series
Example 3
Given …. Find the sum of the infinite geometric series, if it exists.
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1.6A: Geometric Infinite Series

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

9. 1.6A: Geometric Infinite Series
Example 4
Evaluate 𝒌=𝟏 ∞ −𝟓 𝟒 𝟓 𝒌
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1.6A: Geometric Infinite Series

10. 1.6A: Geometric Infinite Series
Your Turn
Evaluate 𝒌=𝟏 ∞ 𝟏 𝟐 𝒌
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1.6A: Geometric Infinite Series

11. 1.6A: Geometric Infinite Series
Assignment
Worksheet
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1.6A: Geometric Infinite Series