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 limit comparison test.
If possible, find the sum of the series .
- DThe series diverges.
All the terms of the series are positive when is large since when and close to 0. Use the limit comparison test to decide whether the series is convergent or divergent.
Suppose and with . What does the limit comparison test tell us about the series ?
- AIt tells us that it is alternating.
- BIt tells us that it is convergent.
- CIt tells us that it is constant.
- DIt tells us that it is divergent.
- EIt tells us nothing.
Let and consider the series . We want to apply the limit comparison test.
Find so that is a positive constant.
Is the series convergent or divergent?