[tex]C= \frac{1}{100} - (\frac{1}{99.100} + \frac{1}{98.99} + ... + \frac{1}{2.3} + \frac{1}{1.2})[/tex]
[tex]C= \frac{1}{100} - (\frac{1}{99} - \frac{1}{100} + \frac{1}{98} - \frac{1}{99} + ... + \frac{1}{2} - \frac{1}{3} + 1 - \frac{1}{2})[/tex]
[tex]C = \frac{1}{100} - (-\frac{1}{100}+ 1)[/tex]
[tex]C = \frac{1}{100} + \frac{1}{100} - 1[/tex]
[tex]C = \frac{-49}{50}[/tex]