Worksheet: Harmonic and p-Series

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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:

If possible, find the sum of the series ∞2(𝑛+1)+23.

  • A3
  • B4
  • CThe series diverges.
  • D92
  • E72

Q2:

Determine whether the series ∞4ln converges or diverges.

Hint: 4ln is equal to 1𝑛ln.

  • AIt diverges.
  • BIt converges.

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 ∞1√𝑛 converges or diverges.

  • AIt diverges.
  • BIt converges.

Q6:

Determine whether the series ∞1√𝑛 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 ∞𝑛𝑛 converges or diverges.

  • AIt diverges.
  • BIt converges.

Q9:

Determine whether the series ∞1𝑛√𝑛 converges or diverges.

  • AIt converges.
  • BIt diverges.

Q10:

State whether the given p-series ∞1𝑛√𝑛 converges or diverges.

  • AIt converges.
  • BIt diverges.

Q11:

Use the 𝑝-series test to determine whether the series ∞√4𝑛5𝑛is divergent or convergent.

  • AConvergent
  • BDivergent

Q12:

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

  • AConvergent
  • BDivergent

Q13:

Use the 𝑝-series test to determine whether the series ∞14𝑛 is divergent or convergent.

  • AConvergent
  • BDivergent

Q14:

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

  • AConvergent
  • BDivergent

Q15:

Use the 𝑝-series test to determine whether the series ∞7𝑛5𝑛 is divergent or convergent.

  • ADivergent
  • BConvergent

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