Convergence Testing and Alternating Series Quiz
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Questions and Answers

Which test compares a given series to a geometric series using the ratios of consecutive terms?

  • Divergence Test
  • Alternating Series Test
  • Ratio Test (correct)
  • Integral Test
  • If the limit of the ratio of consecutive terms of a given series approaches 1, what does it indicate according to the Ratio Test?

  • The series diverges
  • The series converges
  • The test is inconclusive (correct)
  • The Ratio Test is invalid
  • What does the Ratio Test indicate if the limit of the ratio of consecutive terms is a value such that |r| < 1?

  • The series diverges
  • The Ratio Test is invalid
  • The series converges (correct)
  • The test is inconclusive
  • For large values of k, if $a_{k+1} \ approx ra_k$ for large k, what does this imply about the given series?

    <p>The series converges</p> Signup and view all the answers

    What does it mean if a given series is approximately geometric for large k according to the Ratio Test?

    <p>The series converges</p> Signup and view all the answers

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