đề --> $S=\frac{38}{25} + 2.(\frac{9}{20}-\frac{11}{30}+\frac{13}{42}-...-\frac{199}{9900})$
$S= \frac{38}{25} + 2.(\frac{9}{4.5}-\frac{11}{5.6} + \frac{13}{6.7}-...-\frac{199}{99.100})$
$S=\frac{38}{25}+2.(\frac{1}{4}+\frac{1}{5}-\frac{1}{5}-\frac{1}{6}+\frac{1}{6}+....-\frac{1}{99}-\frac{1}{100})$
$S=\frac{38}{25}+2.(\frac{1}{4}-\frac{1}{100})$