Unraveling Divergent Series
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Questions and Answers

Which of the following statements about the series 1 + 2 + 3 + 4 + ⋯ is true?

  • The series is equal to 0
  • The series is divergent (correct)
  • The series is convergent
  • The series has a finite sum
  • What is the nth partial sum of the series 1 + 2 + 3 + 4 + ⋯ ?

  • n(n+1)
  • n(n+1)/2
  • n(n-1)/2 (correct)
  • n^2
  • As n goes to infinity, what happens to the nth partial sum of the series 1 + 2 + 3 + 4 + ⋯ ?

  • It approaches a finite value
  • It oscillates
  • It approaches 0
  • It approaches infinity (correct)
  • What does the formula 1 + 2 + 3 + 4 + ⋯ = -1/12 mean?

    <p>The sum of the series is -1/12</p> Signup and view all the answers

    What is the value of the series 1 + 2 + 3 + 4 + ⋯ according to zeta function regularization and Ramanujan summation?

    <p>-1/12</p> Signup and view all the answers

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