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Lesson Worksheet: Harmonic and 𝑝-Series Mathematics • Higher Education

In this worksheet, we will practice finding the condition for which the 𝑝-series converges, and we will prove the divergence of the harmonic series using the integral test.

Q1:

Determine whether the series 4ln converges or diverges.

Hint: 4ln is equal to 1𝑛ln.

  • AIt diverges.
  • BIt converges.

Q2:

Determine whether the series 1𝑛 converges or diverges.

  • AIt converges.
  • BIt diverges.

Q3:

Determine whether the series 1𝑛 converges or diverges.

  • AIt diverges.
  • BIt converges.

Q4:

Determine whether the series 1𝑛 converges or diverges.

  • AIt converges.
  • BIt diverges.

Q5:

Determine whether the series 𝑛𝑛 converges or diverges.

  • AIt diverges.
  • BIt converges.

Q6:

Determine whether the series 1𝑛𝑛 converges or diverges.

  • AIt converges.
  • BIt diverges.

Q7:

Determine whether the series 𝑛𝑛 converges or diverges.

  • AIt diverges.
  • BIt converges.

Q8:

Determine whether the series 1𝑛 converges or diverges.

  • AIt diverges.
  • BIt converges.

Q9:

State whether the given p-series 1𝑛𝑛 converges or diverges.

  • AIt converges.
  • BIt diverges.

Q10:

Use the 𝑝-series test to determine whether the series 𝑛𝑛 is divergent or convergent.

  • AConvergent
  • BDivergent

This lesson includes 7 additional questions and 45 additional question variations for subscribers.

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