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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

**1. In the Bernoulli's time, what was the current definition of a series?**
**(a)** The finite sum of a divergent series. **(b)** The infinite sum of a convergent series. **(c)** The sum of a finite series of terms. **(d)** The sum of a never-ending series of terms.

**2. What did Cantor's cardinal numbers represent?**
**(a)** Infinite sets. **(b)** Sets of all imaginary numbers. **(c)** Finite series. **(d)** Series of prime numbers.

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

**4. In his later life, what position did Isaac Newton hold?**
**(a)** Professor of philosophy in Paris. **(b)** Warden of the Mint. **(c)** Angelican father. **(d)** Principle science advisor to Charles II.

**5. What did Euler prove about 2²ⁿ + 1?**
**(a)** That the statment is sometimes prime and sometimes composite. **(b)** That the statement is neither prime nor composite. **(c)** That the statement is always a prime number. **(d)** That the statement is always a composite number.

## Short Answer Questions

**1.** Which name does NOT belong?

**2.** Who eventually solved the sum of the successive squared denominator series?

**3.** What did Gauss construct?

**4.** What did Dunham describe as lacking from calculus previous to the mid-19th century?

**5.** Where was George Cantor born?

## Short Essay Questions

**1.** What was the great theorem of this chapter? Describe it briefly.

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

**3.** Summarize in a few sentences, what types of number sets did Cantor prove to be denumerable and non-denumerable.

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

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

**6.** Describe who were Jakob and Johann Bernoulli.

**7.** Describe some of Gauss's work.

**8.** Explain why Eulers sum of Ï€Â²/6 was in some ways surprising.

**9.** What was Gauss's major unpublished achievement in geometry?

**10.** What great theorems and work of Newton did Dunham highlight?

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