1/
a) $\frac{1}{2}$ + $\frac{1}{2.3}$ + $\frac{1}{3.4}$ + ... + $\frac{1}{99.100}$
= $\frac{1}{1.2}$ + $\frac{1}{2.3}$ + $\frac{1}{3.4}$ + ... + $\frac{1}{99.100}$
Ta thấy : $\frac{1}{1.2}$ = 1 - $\frac{1}{2}$
$\frac{1}{2.3}$ = $\frac{1}{2}$ - $\frac{1}{3}$
..........
$\frac{1}{99.100}$ = $\frac{1}{99}$ - $\frac{1}{100}$
= 1 - $\frac{1}{2}$ + $\frac{1}{2}$ - $\frac{1}{3}$ + ... + $\frac{1}{99}$ - $\frac{1}{100}$
= 1 - $\frac{1}{100}$
= $\frac{100}{100}$ - $\frac{1}{100}$
= $\frac{99}{100}$.
