Worksheet: Harmonic and p-Series

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 ) + 2 3 .

  • AThe series diverges.
  • B 9 2
  • C3
  • D4
  • E 7 2

Q2:

Determine whether the series ∞ 4 l n converges or diverges.

Hint: 4 l n is equal to 1 𝑛 l n .

  • AIt diverges.
  • BIt converges.

Q3:

Determine whether the series ∞ 1 𝑛 converges or diverges.

  • AIt converges.
  • BIt diverges.

Q4:

Determine whether the series ∞ 1 𝑛 converges or diverges.

  • AIt diverges.
  • BIt converges.

Q5:

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

  • AIt converges.
  • BIt diverges.

Q6:

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

  • AIt converges.
  • BIt diverges.

Q7:

Determine whether the series ∞ 𝑛 𝑛 converges or diverges.

  • AIt diverges.
  • BIt converges.

Q8:

Determine whether the series ∞ 𝑛 𝑛 converges or diverges.

  • AIt diverges.
  • BIt converges.

Q9:

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

  • AIt converges.
  • BIt diverges.

Q10:

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

  • AIt diverges.
  • BIt converges.

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