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 ) 𝑛 𝑛 + 1 . What is the reason?

  • Abecause the terms are not alternating in sign
  • Bbecause l i m 𝑛 𝑛 + 1 0
  • Cbecause the terms are not decreasing

Q2:

Is the series ( 1 ) ( 𝑛 ) c o s an alternating series?

  • Ayes
  • Bno

Q3:

Determine whether the series 𝑛 𝜋 𝑛 c o s converges or diverges.

  • AIt diverges.
  • BIt converges.

Q4:

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

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

Q5:

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

  • AThe series converges conditionally.
  • BThe series converges absolutely.
  • CThe series diverges.
  • DWe cannot conclude anything.

Q6:

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

  • AIt converges.
  • BIt diverges.

Q7:

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

  • AIt converges.
  • BIt diverges.

Q8:

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

  • AIt diverges.
  • BIt converges.

Q9:

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

  • AIt diverges.
  • BIt converges.

Q10:

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

  • AIt diverges.
  • BIt converges.

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