# Worksheet: Root Test

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

Q1:

Consider the series , where .

Calculate .

• A1
• B
• C0
• D
• E

Hence, determine whether the series converges or diverges.

• AIt converges.
• BIt diverges.

Q2:

Consider the series , where .

Calculate

• A
• B
• C0
• D
• E6

Hence, determine whether the series converges or diverges.

• AIt diverges.
• BIt converges.

Q3:

A series satisfies

What can we conclude about the convergence of the series?

• AThe series converges conditionally.
• BThe series diverges.
• CThe series converges absolutely.
• DWe cannot conclude anything.

Q4:

Consider the series .

Is this an alternating series?

• Ayes
• Bno

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

• Aabsolutely convergent
• Bdivergent
• Cconditionally convergent

Q5:

Consider the series , where the term .

What is ?

What is ?

Use LβHopitalβ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 that for all large values of .
• BIt tells us nothing.
• CIt tells us that and are both zero if is large enough.
• DIt tells us that for all values of .
• EIt tells us that for all large values of .

Is this series convergent or divergent?

• Aconvergent
• Bdivergent