Worksheet: Alternating Series Test

In this worksheet, we will practice determining whether an alternating series is convergent or divergent using the alternating series test.

Q1:

The alternating series test does not apply to the series (1)𝑛𝑛+1. What is the reason?

  • Abecause the terms are not decreasing
  • Bbecause lim𝑛𝑛+10
  • Cbecause the terms are not alternating in sign

Q2:

Is the series (1)(𝑛)cos an alternating series?

  • Ayes
  • Bno

Q3:

Determine whether the series 𝑛𝜋𝑛cos converges or diverges.

  • AIt diverges.
  • BIt converges.

Q4:

What can you conclude about the convergence of the series (1)𝑛+2𝑛+1?

  • AThe series converges conditionally.
  • BThe series converges absolutely.
  • CWe cannot conclude anything.
  • DThe series diverges.

Q5:

What can you conclude about the convergence of the series (1)𝑛+4𝑛+1?

  • AThe series converges conditionally.
  • BWe cannot conclude anything.
  • CThe series converges absolutely.
  • DThe series diverges.

Q6:

Determine whether the series (1)(𝑛+1) converges or diverges.

  • AIt converges.
  • BIt diverges.

Q7:

Determine whether the series (1)5𝑛! converges or diverges.

  • AIt converges.
  • BIt diverges.

Q8:

Determine whether the series (1)5𝑛+15𝑛+2 converges or diverges.

  • AIt diverges.
  • BIt converges.

Q9:

Determine whether the series (1)3𝑛+13𝑛+2 converges or diverges.

  • AIt converges.
  • BIt diverges.

Q10:

Determine whether the series (1)1𝑛sin converges or diverges.

  • AIt diverges.
  • BIt converges.

Q11:

Determine whether the series 𝑛!(3) is convergent or divergent.

  • AThe series is divergent.
  • BThe series is convergent.

Q12:

Determine whether the series (1)𝑛! is convergent or divergent.

  • AThe series is convergent.
  • BThe series is divergent.

Q13:

Determine whether the series (1)4𝑛+25𝑛+3𝑛 is convergent or divergent.

  • AThe series is divergent.
  • BThe series is convergent.

Q14:

Determine whether the series 𝜋𝑛sin is convergent or divergent.

  • AThe series is convergent.
  • BThe series is divergent.

Q15:

Determine whether the series (1)2𝑛𝑛+3 is convergent or divergent.

  • AThe series is divergent.
  • BThe series is convergent.

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