# Lesson Worksheet: Comparison Test for Series Mathematics • Higher Education

In this worksheet, we will practice determining whether a series is convergent or divergent by comparing it to a series of known convergence using the comparison test.

Q1:

Use the comparison test to decide whether the series is convergent or divergent.

• Aconvergent
• Bdivergent

Q2:

Let . As , we see that , which suggests that is a divergent series. Verify this by finding the first integer where . You should check that this inequality remains true for all larger .

Q3:

Consider the series .

Do the terms of this sequence tend to 0 as ?

• ANo
• BYes

Is the series convergent or divergent?

• BConvergent

Q4:

Suppose is a series with the property that there is an integer such that for all indices .

Does it follow that all the terms of the series are positive?

• ANo
• BYes

Does it follow that the number of negative terms is finite?

• AYes
• BNo

Is the series convergent?

• ANo
• BIt is not possible to tell.
• CYes

Is the series convergent if the inequality is instead?

• ANo
• BYes
• CIt is not possible to tell.

Q5:

Use the comparison test to determine whether is convergent or divergent.

• Aconvergent
• Bdivergent

Q6:

Use the comparison test to decide whether the series is convergent or divergent.

• Bconvergent

Q7:

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

• BConvergent

Q8:

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

• BConvergent

Q9:

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

• AConvergent
• BDivergent

Q10:

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