# Lesson Worksheet: The 𝑛th Term Divergence Test Mathematics • Higher Education

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.

Q4:

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.

Q6:

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

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

Q7:

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

• AThe test fails.
• BThe series is divergent.

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:

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

• ATrue
• BFalse

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