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This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

Multiple Choice Questions

1. What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?
(a) Both series were composed of successively smaller terms.
(b) Both series were divergent.
(c) Both series were composed of successively larger terms.
(d) Both series were convergent.

2. What was described as true about the series 1 + 1/2 + 1/6 + 1/10 + 1/15 + 1/21?
(a) It's a divergent series with a sum of 2.
(b) It's a convergent series of cubic numbers.
(c) It's a convergent series of triangular numbers.
(d) It's a divergent series squared numbers.

3. What did Gauss do with his best work?
(a) He did not publish it.
(b) He gave it to his son to publish.
(c) He gave it to his students.
(d) He published it.

4. What was true when Euler used n = 5 in the statement 2²ⁿ + 1?
(a) The statement was a perfect number.
(b) The statement was a composite number.
(c) The statement was not a prime number.
(d) The statement was a prime number.

5. What did Cantor struggle with later in his life?
(a) Blindness.
(b) Mental illness.
(c) Seizures.
(d) Leukemia.

Short Answer Questions

1. What sum did Euler find for the series?

2. Which of the following is a series that the Bernoullis proposed did not converge on a finite sum?

3. What series was Euler most famous for?

4. Which name does NOT belong?

5. Where was George Cantor born?

Short Essay Questions

1. Describe who were Jakob and Johann Bernoulli.

2. Explain any methods used by Cantor that were unsuccessful.

3. Describe some of Gauss's work.

4. Describe what mathematical and artistic movements are focused on in the second half of the 19th century.

5. Describe Newton's days in Cambridge and what he eventually came to discover.

6. What were the two transfinite cardinals discovered by Cantor, and what method did he use to determine them?

7. Give an example of a series who's sum is still unknown.

8. Where did the center of mathematical thinking shift to in the !7th Century, and who are the major scholars of this time period?

9. What was Gauss's major unpublished achievement in geometry?

10. Why did Euler start working on the sum of series?

(see the answer keys)

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