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Math Induction: Truth Beyond Finiteness
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Math Induction: Truth Beyond Finiteness

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Questions and Answers

What is the main objective of the proof of sum of squares by induction?

  • To prove the sum of squares is always an even number
  • To show that the sum of squares is equal to ninjas
  • To prove the formula for the sum of squares using mathematical induction (correct)
  • To prove the sum of squares is always finite

    • What is the claim in the proof of sum of cubes by induction?

  • k=1 k3 = n · (n + 1) 2 (correct)
  • k=1 k5 = n · (n + 1) 2
  • k=1 k4 = n · (n + 1) 2
  • k=1 k2 = n · (n + 1) 2

    • What is the purpose of the base step in a proof by induction?

  • To prove the statement is true for only one value of n (correct)
  • To prove the statement is true for all negative integers
  • To prove the statement is true for all positive integers
  • To prove the statement is true for all real numbers

    • What is the purpose of the inductive step in a proof by induction?

    <p>To prove the statement is true for all positive integers</p> Signup and view all the answers

    What is the formula for the sum of squares proved in the given text?

    <p>12 + 22 + 32 + · · · + n2 = n · (n + 1) 2</p> Signup and view all the answers

    What is the assumption made in the inductive step of the proof of sum of cubes by induction?

    <p>Assume P(n) is true</p> Signup and view all the answers

    What is the goal of the inductive step in the proof of sum of cubes by induction?

    <p>To prove P(n+1) is true if P(n) is true</p> Signup and view all the answers

    What is the role of mathematical induction in the proof of sum of squares and sum of cubes?

    <p>To prove the statements are true for all positive integers</p> Signup and view all the answers

    What is the format of the proof of sum of squares and sum of cubes by induction?

    <p>Base step and inductive step</p> Signup and view all the answers

    What is the main difference between the proof of sum of squares and sum of cubes by induction?

    <p>The formula for the sum of squares and sum of cubes</p> Signup and view all the answers

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