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

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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 π‘Žβ†’0 as π‘›β†’βˆž, then βˆžοŠοŠ²οŠ¦οŠο„šπ‘Ž is convergent.

  • ATrue
  • BFalse

Q2:

What can we conclude by applying the 𝑛th term divergence test in the series βˆžοŠοŠ²οŠ§οŠ¨ο„š3π‘›βˆš6𝑛+4𝑛+5?

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

Q3:

What can we conclude by applying the 𝑛th term divergence test in the series βˆžοŠοŠ²οŠ§ο„š3𝑛cos?

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

Q4:

What can we conclude by applying the 𝑛th term divergence test in the series βˆžοŠοŠ²οŠ§οŠ¨οŠοŠ¨οŠο„š(5𝑛+3)(7𝑛+2)?

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

Q5:

What can we conclude by applying the 𝑛th term divergence test in the series βˆžοŠοŠ²οŠ§ο„š2𝑛3𝑛ln?

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

Q6:

What can we conclude by applying the 𝑛th term divergence test in the series βˆžοŠοŠ²οŠ§οŠ¨ο„š2𝑛6𝑛+4?

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

Q7:

Using the 𝑛th term test, determine whether the series βˆžοŠοŠ²οŠ§ο„š(𝑛+2)!(2𝑛)! is divergent or the test fails.

  • AThe test fails.
  • BThe series is divergent.

Q8:

Using the 𝑛th term test, determine whether the series βˆžοŠοŠ²οŠ¦οŠ¨ο„šπ‘›π‘›+1 is divergent or the test fails.

  • AThe test fails.
  • BThe series is divergent.

Q9:

Using the nth term test, determine whether the series βˆžοŠοŠ²οŠ¦οŠοŠο„š43 is divergent or the test fails.

  • AThe test fails.
  • BThe series is divergent.

Q10:

True or False: If π‘Žβ†’0 as π‘›β†’βˆž, then the 𝑛th term divergence test fails for βˆžοŠοŠ²οŠ¦οŠο„šπ‘Ž.

  • ATrue
  • BFalse

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