# Worksheet: Limit Comparison Test

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 limit comparison test.

Q1:

If possible, find the sum of the series .

• A2
• BThe series diverges.
• C
• D1
• E

Q2:

All the terms of the series are positive when is large since when and close to 0. Use the limit comparison test to decide whether the series is convergent or divergent.

• Aconvergent
• Bdivergent

Q3:

Suppose and with . What does the limit comparison test tell us about the series ?

• AIt tells us nothing.
• BIt tells us that it is convergent.
• CIt tells us that it is alternating.
• DIt tells us that it is constant.
• EIt tells us that it is divergent.

Q4:

Let and consider the series . We want to apply the limit comparison test.

Find so that is a positive constant.

• A2
• B
• C
• D
• E1

Is the series convergent or divergent?

• Aconvergent
• Bdivergent

Q5:

For the series , use the limit comparison test to determine whether the series converges or diverges.

• AIt diverges.
• BIt converges.

Q6:

For the series , use the limit comparison test to determine whether the series converges or diverges.

• AIt converges.
• BIt diverges.

Q7:

For the series , use the limit comparison test to determine whether the series converges or diverges.

• AIt diverges.
• BIt converges.

Q8:

For the series , use the limit comparison test to determine whether the series converges or diverges.

• AIt diverges.
• BIt converges.

Q9:

For the series , use the limit comparison test to determine whether the series converges or diverges.

• AIt converges.
• BIt diverges.

Q10:

For the series , determine whether the series converges or diverges using the limit comparison test.

• AIt diverges.
• BIt converges.

Q11:

Using the limit comparison test, determine whether the series is convergent or divergent.

• AConvergent
• BDivergent

Q12:

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

• BConvergent

Q13:

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

• AConvergent
• BDivergent

Q14:

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

• AConvergent
• BDivergent

Q15:

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