# 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 , where for some integers .

Calculate .

• A
• B
• C
• D2
• E0

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 diverges.
• BIt converges.

Q3:

Consider the series .

Calculate .

• A
• B
• C
• D
• E0

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

Q5:

True or False: The series is convergent by the ratio test.

• Afalse
• Btrue

Q6:

Consider the series . Determine whether the series converges or diverges.

• AIt converges.
• BIt diverges.

Q7:

Consider the series . Determine whether the series converges or diverges.

• AIt converges.
• BIt diverges.

Q8:

Consider the series . Determine whether the series converges or diverges.

• AIt diverges.
• BIt converges.

Q9:

Consider the series . Determine whether the series converges or diverges.

• AIt diverges.
• BIt converges.

Q10:

Consider the series . Determine whether the series converges or diverges.

• AIt converges.
• BIt diverges.

Q11:

Using the ratio test, determine whether the series is convergent, divergent, or whether the test is inconclusive.

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

Q12:

Given that is a positive integer, find the set of values of for which the series is convergent.

• A
• B
• C
• D
• E

Q13:

Using the ratio test, determine whether the series is convergent, divergent, or whether the test is inconclusive.

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

Q14:

Using the ratio test, determine whether the series is convergent, divergent, or whether the test is inconclusive.

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

Q15:

The terms of a series are defined by the equations and . Using the ratio test, determine whether the series is convergent, divergent, or whether the test is inconclusive.

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