# Worksheet: Root Test

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

**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