$\frac{1}{1.2}$ + $\frac{1}{3.4}$ + $\frac{1}{5.6}$ + ... +$\frac{1}{99.100}$
= = 1 - $\frac{1}{2}$ + $\frac{1}{3}$ - $\frac{1}{4}$ + $\frac{1}{5}$ - $\frac{1}{6}$ + ... + $\frac{1}{99}$ - $\frac{1}{100}$
= 1 + $\frac{1}{2}$ + $\frac{1}{3}$ + $\frac{1}{4}$ + $\frac{1}{5}$ + $\frac{1}{6}$ + ... + $\frac{1}{99}$ + $\frac{1}{100}$ - 2( $\frac{1}{2}$ + $\frac{1}{4}$ + $\frac{1}{6}$ + ... + $\frac{1}{100}$)
= 1 + $\frac{1}{2}$ + $\frac{1}{3}$ + $\frac{1}{4}$ + $\frac{1}{5}$ + $\frac{1}{6}$ + ... + $\frac{1}{99}$ + $\frac{1}{100}$ - ( 1 + $\frac{1}{2}$ + $\frac{1}{3}$ + $\frac{1}{4}$ + $\frac{1}{5}$ + $\frac{1}{6}$ + ... + $\frac{1}{50}$)
=( $\frac{1}{51}$ + $\frac{1}{52}$ + $\frac{1}{53}$ + $\frac{1}{54}$ + $\frac{1}{55}$ + ... + $\frac{1}{100}$)
