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AP®MathsCollege BoardCalculus BCExam QuestionsUnit 10: Infinite Sequences and SeriesIntroduction to Infinite Series

Introduction to Infinite Series (College Board AP® Calculus BC): Exam Questions

11 mins11 questions
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1
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For what values of q will the series sum from n equals 1 to infinity of open parentheses q over 7 close parentheses to the power of n converge?

  • q less than 7

  • negative 7 less than q less than 7 only

  • q greater or equal than 7

  • q greater than 7

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2
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For what values of q will the series sum from n equals 1 to infinity of 1 over n to the power of 5 q end exponent converge?

  • q less than 1 fifth

  • negative 1 fifth less than q less than 1 fifth only

  • q greater or equal than 1 fifth

  • q greater than 1 fifth

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3
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The sum of the infinite geometric series sum from n equals 0 to infinity of 2 times open parentheses 3 over 4 close parentheses to the power of n is

  • 4 over 7

  • 8 over 7

  • 4

  • 8

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1
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For what values of q will the series sum from n equals 1 to infinity of 1 over n to the power of 4 q end exponent and sum from n equals 1 to infinity of open parentheses q over 4 close parentheses to the power of n both converge?

  • negative 4 less than q less than 4 only

  • negative 1 fourth less than q less than 1 fourth only

  • 1 fourth less than q less than 4 only

  • q less than 1 fourth and q greater than 4

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2
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The sum of the infinite geometric series 7 over 2 plus 21 over 16 plus 63 over 128 plus fraction numerator 189 over denominator 1 comma 024 end fraction plus... is

  • 5.45

  • 5.50

  • 5.55

  • 5.60

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3
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Which of the following series are convergent?

I. space 1 plus 1 over 2 cubed plus 1 over 3 cubed plus... plus 1 over n cubed plus...

II. space 1 plus 1 half plus 1 third plus... plus 1 over n plus...

III. space 1 minus 1 half plus 1 over 2 squared minus... plus open parentheses negative 1 close parentheses to the power of n plus 1 end exponent over 2 to the power of n minus 1 end exponent plus...

  • I only

  • I and III only

  • II and III only

  • I, II, and III

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41 mark

For what values of x does the infinite series 1 plus 2 to the power of x plus 3 to the power of x plus... plus n to the power of x plus... converge?

  • No values of x

  • x less than negative 1

  • x equals negative 1

  • x greater than negative 1

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5
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The sum of the infinite geometric series sum from n equals 1 to infinity of 4 times open parentheses negative 3 over 5 close parentheses to the power of n is

  • negative 6

  • negative 3 over 2

  • 5 over 2

  • 10

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1
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For what values of q will the series sum from n equals 1 to infinity of space fraction numerator 3 over denominator open parentheses n to the power of q over 5 end exponent close parentheses end fraction and sum from n equals 0 to infinity of open parentheses fraction numerator 3 q over denominator 5 end fraction close parentheses to the power of n both converge?

  • negative 5 over 3 less than q less than 5 over 3

  • 1 fifth less than q less than 5 over 3

  • 5 over 3 less than q less than 5

  • There are no such values of q.

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2
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A function f is defined in power series form as f open parentheses x close parentheses equals sum from n equals 0 to infinity of open parentheses negative x over 5 close parentheses to the power of n. What is the value of f open parentheses 2 close parentheses?

  • negative 2 over 5

  • 5 over 7

  • 5 over 3

  • f open parentheses 2 close parentheses does not exist

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3
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For what integer k, where k greater than 4, will the series sum from n equals 1 to infinity of open parentheses k over 7 close parentheses to the power of n and sum from n equals 1 to infinity of open parentheses negative 1 close parentheses to the power of k n end exponent over n both converge?

  • 8

  • 7

  • 6

  • 5

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