Worksheet: Conditional and Absolute Convergence

In this worksheet, we will practice determining if a series is absolutely convergent, conditionally convergent, or divergent.

Q1:

Consider the series (1)2𝑛+1.

Decide whether the series is absolutely convergent, conditionally convergent, or divergent.

  • ADivergent
  • BConditionally convergent
  • CAbsolutely convergent

Q2:

Consider the series (𝑛)(2)cos.

Decide whether the series is absolutely convergent, conditionally convergent, or divergent.

  • AAbsolutely convergent
  • BConditionally convergent
  • CDivergent

Q3:

State whether the series (1)((2𝑛+1)(2𝑛))lnln converges absolutely, conditionally, or not at all.

  • AIt converges absolutely.
  • BIt does not converge at all.
  • CIt converges conditionally.

Q4:

State whether the series (1)3𝑛+13𝑛+2 converges absolutely, conditionally, or not at all.

  • AIt converges conditionally.
  • BIt converges absolutely.
  • CIt does not converge at all.

Q5:

State whether the series (1)2𝑛+1 converges absolutely, conditionally, or not at all.

  • AIt converges absolutely.
  • BIt converges conditionally.
  • CIt does not converge at all.

Q6:

State whether the series (1)1𝑛+21𝑛+3 converges absolutely, conditionally, or not at all.

  • AIt converges conditionally.
  • BIt does not converge at all.
  • CIt converges absolutely.

Q7:

State whether the series (1)𝑛 converges absolutely, conditionally, or not at all.

  • AIt converges absolutely.
  • BIt does not converge at all.
  • CIt converges conditionally.

Q8:

Consider the series (1)4𝑛1.

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

  • AConditionally convergent
  • BDivergent
  • CAbsolutely convergent

Q9:

Consider the series (1)𝑛+1. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

  • AConditionally convergent
  • BDivergent
  • CAbsolutely convergent

Q10:

Consider the series 𝑛𝑛sin. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

  • AConditionally convergent
  • BAbsolutely convergent
  • CDivergent

Q11:

Determine if the series (2)3 is absolutely convergent, conditionally convergent, or divergent.

  • AAbsolutely convergent
  • BConditionally convergent
  • CDivergent

Q12:

Determine if the series (1)3𝑛+6𝑛+124𝑛+1 is absolutely convergent, conditionally convergent, or divergent.

  • AAbsolutely convergent
  • BConditionally convergent
  • CDivergent

Q13:

Determine if the series 4(1)𝑛+1 is absolutely convergent, conditionally convergent, or divergent.

  • AAbsolutely convergent
  • BConditionally convergent
  • CDivergent

Q14:

Determine if the series (1)13(𝑛)ln is absolutely convergent, conditionally convergent, or divergent.

  • ADivergent
  • BConditionally convergent
  • CAbsolutely convergent

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