# Worksheet: Infinite Series

In this worksheet, we will practice representing an infinite series in sigma notation after defining it.

Q1:

Given that , determine whether the infinite series is convergent or divergent.

• AConvergent
• BDivergent

Q2:

Given that , determine whether the infinite series is convergent or divergent.

• BConvergent

Q3:

Express the series using sigma notation.

• A
• B
• C
• D
• E

Q4:

Which of the following series is not equivalent to ?

• A
• B
• C
• D
• E

Q5:

Which of the following is an equivalent expression for the infinite series ?

• A
• B
• C
• D
• E

Q6:

Express the series using sigma notation.

• A
• B
• C
• D
• E

Q7:

Express the series using an index of instead of .

• A
• B
• C
• D
• E

Q8:

Given that , determine whether the infinite series is convergent or divergent.

• BConvergent

Q9:

Which of the following describes the relationship between an infinite series and a sequence?

• AAn infinite series always takes the value of the largest term in an infinite sequence.
• BAn infinite sequence is the sum of the terms in an infinite series.
• CAn infinite series is the sum of the terms in an infinite sequence.
• DAn infinite series is a sequence which has an infinite number of terms.
• EAn infinite series is the product of the terms in an infinite sequence.

Q10:

Which of the following is an equivalent expression for the infinite series ?

• A
• B
• C
• D
• E

Q11:

Express the series as a series that starts at .

• A
• B
• C
• D
• E

Q12:

Which of the following is an example of an infinite series?

• A
• B
• C
• D
• E

Q13:

Given that is a constant, express the series using sigma notation.

• A
• B
• C
• D
• E

Q14:

Which of the following series is equivalent to ?

• A
• B
• C
• D
• E

Q15:

Given that is a constant, which of the following is not an equivalent expression to the infinite series ?

• A
• B
• C
• D
• E

Q16:

Which of the following series is equivalent to ?

• A
• B
• C
• D
• E