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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

**1. What did Euler's sum surprisingly connect?**
**(a)** The area under a curve. **(b)** The squares of area and square roots. **(c)** The area of squares and the area of circles. **(d)** The circumference of a circle and right triangles.

**2. What did Cantor suspect about transfinite cardinals?**
**(a)** That there are transfinite cardinals even greater than c. **(b)** That the sum of the series is infinite. **(c)** That there are transfinite cardinals much less than c. **(d)** That the sum of the series is finite.

**3. What great theorem is presented by Dunham in this chapter?**
**(a)** A theorem on finite series developed by Johann Bernoulli. **(b)** A theorem on series developed by Jakob and published by Johann Bernoulli. **(c)** An improvement on Leibniz's caluclus as presented by Jakob Bernoulli. **(d)** A theorem on infinite series published by Jakob Bernoulli.

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

**5. On who's work did Euler base his number theory?**
**(a)** Newton's. **(b)** Bernoulli's. **(c)** Leibniz's. **(d)** Fermat's.

## Short Answer Questions

**1.** What was similar about both Euler and Gauss as children?

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

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

**4.** Who else, besides Newton, independently discovered a calculus method?

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

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