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 .
- 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