Lesson Worksheet: Comparison Test for Series Mathematics
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 comparison test.
Q1:
Use the comparison test to decide whether the series is convergent or divergent.
- Aconvergent
- Bdivergent
Q2:
Let . As , we see that , which suggests that is a divergent series. Verify this by finding the first integer where . You should check that this inequality remains true for all larger .
Q3:
Consider the series .
Do the terms of this sequence tend to 0 as ?
- AYes
- BNo
Is the series convergent or divergent?
- ADivergent
- BConvergent
Q4:
Suppose is a series with the property that there is an integer such that for all indices .
Does it follow that all the terms of the series are positive?
- ANo
- BYes
Does it follow that the number of negative terms is finite?
- AYes
- BNo
Is the series convergent?
- ANo
- BIt is not possible to tell.
- CYes
Is the series convergent if the inequality is instead?
- ANo
- BYes
- CIt is not possible to tell.
Q5:
Use the comparison test to determine whether is convergent or divergent.
- Aconvergent
- Bdivergent
Q6:
Use the comparison test to decide whether the series is convergent or divergent.
- Adivergent
- Bconvergent
Q7:
Use the comparison test to determine whether the series is convergent or divergent.
- ADivergent
- BConvergent
Q8:
Use the comparison test to determine whether the series is convergent or divergent.
- ADivergent
- BConvergent
Q9:
Use the comparison test to determine whether the series is convergent or divergent.
- AConvergent
- BDivergent
Q10:
Use the comparison test to determine whether the series is convergent or divergent.
- ADivergent
- BConvergent
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