# Lesson Worksheet: Root Test Mathematics

In this worksheet, we will practice determining if a series is convergent or divergent using the root test.

Q1:

Consider the series , where .

Calculate .

• A
• B0
• C1
• D
• E

Hence, determine whether the series converges or diverges.

• AIt converges.
• BIt diverges.

Q2:

Consider the series , where .

Calculate

• A
• B6
• C0
• D
• E

Hence, determine whether the series converges or diverges.

• AIt converges.
• BIt diverges.

Q3:

A series satisfies

What can we conclude about the convergence of the series?

• AWe cannot conclude anything.
• BThe series diverges.
• CThe series converges absolutely.
• DThe series converges conditionally.

Q4:

Consider the series .

Is this an alternating series?

• AYes
• BNo

Is this series absolutely convergent, conditionally convergent, or divergent?

• AAbsolutely convergent
• BConditionally convergent
• CDivergent

Q5:

Consider the series , where the term .

What is ?

What is ?

Use l’Hopital’s rule to determine the value of the limit , where is a constant.

What does the previous result tell you about the values of and , where is an integer?

• AIt tells us nothing.
• BIt tells us that for all values of .
• CIt tells us that for all large values of .
• DIt tells us that for all large values of .
• EIt tells us that and are both zero if is large enough.

Using the comparison test, is this series convergent or divergent?

• AConvergent
• BDivergent