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 𝑎0 as 𝑛, then 𝑎 is convergent.

  • Atrue
  • Bfalse

Q2:

What can we conclude by applying the 𝑛th term divergence test in the series (5𝑛+3)(7𝑛+2)?

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

Q3:

What can we conclude by applying the 𝑛th term divergence test in the series 3𝑛6𝑛+4𝑛+5?

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

Q4:

What can we conclude by applying the 𝑛th term divergence test in the series 3𝑛cos?

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

Q5:

What can we conclude by applying the 𝑛th term divergence test in the series 2𝑛3𝑛ln?

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

Q6:

What can we conclude by applying the 𝑛th term divergence test in the series 2𝑛6𝑛+4?

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

Q7:

True or False: If 𝑎0 as 𝑛, then the 𝑛th term divergence test fails for 𝑎.

  • ATrue
  • BFalse

Q8:

Using the 𝑛th term test, determine whether the series 𝑛𝑛+1 is divergent or the test fails.

  • AThe test fails.
  • BThe series is divergent.

Q9:

Using the nth term test, determine whether the series 43 is divergent or the test fails.

  • AThe test fails.
  • BThe series is divergent.

Q10:

Using the 𝑛th term test, determine whether the series (𝑛+2)!(2𝑛)! is divergent or the test fails.

  • AThe test fails.
  • BThe series is divergent.

Q11:

Use the 𝑛th term divergence test to determine whether the series 𝑛𝑛6𝑛+𝑛 is divergent or whether the test is inconclusive.

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

Q12:

Use the 𝑛th term divergence test to determine whether the series 3(2𝑛)cos is divergent or whether the test is inconclusive.

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

Q13:

Use the 𝑛th term divergence test to determine whether the series 35 is divergent or whether the test is inconclusive.

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

Q14:

Use the 𝑛th term divergence test to determine whether the series 3𝑛7𝑛+2𝑛 is divergent or whether the test is inconclusive.

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

Q15:

Use the 𝑛th term divergence test to determine whether the series 𝑛!2 is divergent or whether the test is inconclusive.

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

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