# 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.

- ADivergent
- 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.

- ADivergent
- 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