# 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 converges or diverges.

Hint: is equal to .

• AIt diverges.
• BIt converges.

Q2:

Determine whether the series converges or diverges.

• AIt converges.
• BIt diverges.

Q3:

Determine whether the series converges or diverges.

• AIt diverges.
• BIt converges.

Q4:

Determine whether the series converges or diverges.

• AIt converges.
• BIt diverges.

Q5:

Determine whether the series converges or diverges.

• AIt diverges.
• BIt converges.

Q6:

Determine whether the series converges or diverges.

• AIt converges.
• BIt diverges.

Q7:

Determine whether the series converges or diverges.

• AIt diverges.
• BIt converges.

Q8:

Determine whether the series converges or diverges.

• AIt diverges.
• BIt converges.

Q9:

State whether the given p-series converges or diverges.

• AIt converges.
• BIt diverges.

Q10:

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

• AConvergent
• BDivergent

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