# Worksheet: The nth Term Divergence Test

In this worksheet, we will practice applying the nth term test for divergence which states that a series diverges if the limit of its nth term does not approach zero.

**Q1: **

True or False: If as , then is convergent.

- Atrue
- Bfalse

**Q2: **

What can we conclude by applying the term divergence test in the series ?

- AThe series diverges.
- BThe divergence test is inconclusive.

**Q3: **

What can we conclude by applying the term divergence test in the series ?

- AThe series diverges.
- BThe divergence test is inconclusive.

**Q5: **

What can we conclude by applying the term divergence test in the series ?

- AThe series converges.
- BThe divergence test is inconclusive.

**Q7: **

True or False: If as , then the term divergence test fails for .

- ATrue
- BFalse

**Q8: **

Using the term test, determine whether the series is divergent or the test fails.

- AThe test fails.
- BThe series is divergent.

**Q9: **

Using the nth term test, determine whether the series is divergent or the test fails.

- AThe test fails.
- BThe series is divergent.

**Q10: **

Using the term test, determine whether the series is divergent or the test fails.

- AThe test fails.
- BThe series is divergent.

**Q11: **

Use the term divergence test to determine whether the series is divergent or whether the test is inconclusive.

- AThe test is inconclusive.
- BThe series is divergent.

**Q12: **

Use the term divergence test to determine whether the series is divergent or whether the test is inconclusive.

- AThe test is inconclusive.
- BThe series is divergent.

**Q14: **

Use the term divergence test to determine whether the series is divergent or whether the test is inconclusive.

- AThe test is inconclusive.
- BThe series is divergent.

**Q15: **

- AThe test is inconclusive.
- BThe series is divergent.