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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 did Dunham describe about the following series 1 + 2 + 3 + 4. . .?**
**(a)** The sum converges to a finite term. **(b)** The sum converges to infinity. **(c)** The sum grows ever smaller. **(d)** The sum diverges to infinity.

**2. 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.

**3. Which of the following was one of Gauss' early discoveries?**
**(a)** A proof that the Pythagorean Theorem was correct. **(b)** A demonstration of the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ . . . 1/k³ . . **(c)** A way to construct a regular 17-sided polygon. **(d)** A method to simplify Newton's calulus.

**4. Which word best describes Newton's childhood?**
**(a)** Hard. **(b)** Troubled. **(c)** Cold. **(d)** Simple.

**5. Who was Euler's teacher?**
**(a)** Gottfried Leibniz. **(b)** Jakob Bernoulli. **(c)** Isaac Newton. **(d)** Johann Bernoulli.

## Short Answer Questions

**1.** What didn't Euler attempt?

**2.** Who encourages Newton during his studies at Cambridge?

**3.** What did mathematicians want to perfect in the mid-19th century?

**4.** What did British scholars accuse Leibniz of?

**5.** What great theorem is presented by Dunham in this chapter?

## Short Essay Questions

**1.** What was Gauss's major unpublished achievement in geometry?

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

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

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

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

**6.** Describe some of the characteristics of Leonhard Euler, and what made him successful.

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

**8.** Describe what the Bernoullis discovered about series, and give an example.

**9.** Describe the great theorem explained by Dunham in this chapter.

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

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