Chapter 1.1, Problem 35E

Use inductive reasoning to make a conjecture about the next three sums, and then perform the calculations to verify that your conjecture is true.

$\begin{array}{l}1+\frac{1}{2}=\frac{3}{2}\\ 1+\frac{1}{2}+\frac{1}{2\cdot 3}=\frac{5}{3}\\ 1+\frac{1}{2}+\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}=\frac{7}{4}\\ 1+\frac{1}{2}+\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\frac{1}{4\cdot 5}=?\\ 1+\frac{1}{2}+\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\frac{1}{4\cdot 5}+\frac{1}{5\cdot 6}=?\\ 1+\frac{1}{2}+\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\frac{1}{4\cdot 5}+\frac{1}{5\cdot 6}+\frac{1}{6\cdot 7}=?\end{array}$