Lesson Worksheet: Monotone Convergence Theorem Mathematics
In this worksheet, we will practice using the monotone convergence theorem to test for convergence.
Q1:
Which of the following describes the least upper bound of a subset of numbers?
- Athe number so that if for all , then
- Bthe number so that if , then
- Cthe number so that if for all , then
- Dthe largest number amongst all
- Ethe smallest number amongst all
Q2:
Suppose is a subset of real numbers that has an upper bound .
Suppose that is a least upper bound of . Which of the following relations between and must be true?
- A
- B
- C
- D
- E
Suppose is a second least upper bound for . Which of the following relations between and must be true?
- A
- B
- C
- D
Q3:
Consider the sequence for .
Is ?
- ANo
- BYes
Is ?
- ANo
- BYes
Define and by and . Write in simplified form.
- A
- B
- C
- D
- E
Using the above and the quadratic formula, find the smallest integer so that whenever .
Q4:
Is the sequence increasing, decreasing, or neither?
- A is neither increasing nor decreasing.
- B is decreasing.
- C is increasing.
Q5:
The term of a sequence is . If , is ?
- ANo
- BYes
Q6:
Use , , or to complete the following: A sequence with term is constant if for each .
- A
- B
- C
Q7:
Use , , or to complete the following: A sequence with term is strictly increasing if for each .
- A
- B
- C
Q8:
Is the sequence increasing, decreasing, or neither?
- A is decreasing.
- B is neither increasing nor decreasing.
- C is increasing.
Q9:
Is the sequence , where increasing, decreasing, or neither?
- A is decreasing.
- B is neither increasing nor decreasing.
- C is increasing.
Q10:
Is the sequence increasing, decreasing, or neither?
- Aneither increasing nor decreasing
- Bincreasing
- Cdecreasing