Worksheet: Ratio Test

In this worksheet, we will practice determining if a series is convergent or divergent using the ratio test.

Q1:

Consider the series 𝑛 = 0 𝑛 𝑇 , where 𝑇 = 𝑛 + 𝑏 𝑐 𝑛 𝑛 for some integers 𝑏 , 𝑐 > 1 .

Calculate l i m 𝑛 𝑛 + 1 𝑛 | | | 𝑇 𝑇 | | | .

  • A
  • B0
  • C2
  • D
  • E 1 2

Hence, decide whether the series converges or diverges.

  • AIt diverges.
  • BIt converges.

Q2:

Consider the series , where for some integers , .

Calculate .

Hence, decide whether the series converges or diverges.

  • AIt converges.
  • BIt diverges.

Q3:

Consider the series .

Calculate .

  • A
  • B0
  • C
  • D
  • E

Hence, determine whether the series converges or diverges.

  • AIt converges.
  • BIt diverges.

Q4:

A series satisfies . What can you conclude about the convergence of the series?

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

Q5:

True or False: The series 𝑛 = 1 2 1 𝑛 + 1 is convergent by the ratio test.

  • Afalse
  • Btrue

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