Chapter 1.2, Problem 30E

Applying What You’ve Learned.

In each of the next four exercises, we give you a series of numerical equations. Make a conjecture as to what the next two equations in the pattern are. Check your conjecture with a calculator.

a. $\frac{1}{1\times 2}+\frac{1}{2\times 3}=\frac{2}{3}$

b. $\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}=\frac{3}{4}$

c. $\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+\frac{1}{4\times 5}=\frac{4}{5}$