Compute in simpliest form:
\(\left(1 - \frac{1}{3}\right) + \left(\frac{1}{3} - \frac{1}{5}\right) + \left(\frac{1}{5} - \frac{1}{7}\right) + \left(\frac{1}{7} - \frac{1}{9}\right) + \cdots + \left(\frac{1}{17} - \frac{1}{19}\right)\)
Note that we can write this in a slightly different manner
1 + (-1/3 + 1/3) + (-1/5 + 1/5) + (-1/7 + 1/7) +......+ (-1/17 + 1/17) - 1/19 =
1 - 1/19 =
18 /19
