\(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+.......+\frac{1}{49.50}\)

\(=\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+......+\frac{1}{50}\)

\(=\frac{1}{10}-\frac{1}{50}=\frac{2}{25}\)

a, \(\dfrac{10}{17}\) + \(\dfrac{5}{-13}\) - \(\dfrac{11}{25}\) + \(\dfrac{7}{17}\) - \(\dfrac{8}{13}\)

= ( \(\dfrac{10}{17}\) + \(\dfrac{7}{17}\)) - ( \(\dfrac{5}{13}\) + \(\dfrac{8}{13}\)) - \(\dfrac{11}{25}\)

= \(\dfrac{17}{17}\) - \(\dfrac{13}{13}\) - \(\dfrac{11}{25}\)

= 1 - 1 - \(\dfrac{11}{25}\)

= - \(\dfrac{11}{25}\)

b, 0,3 - \(\dfrac{93}{7}\) - 70% - \(\dfrac{4}{7}\)

= 0,3 - 0,7 - ( \(\dfrac{93}{7}+\dfrac{4}{7}\))

= - 0,4 - \(\dfrac{97}{7}\)
= - \(\dfrac{2}{5}\) - \(\dfrac{97}{7}\)

= - \(\dfrac{499}{35}\)

c, \(\dfrac{1}{8}\) + \(\dfrac{1}{24}\) + \(\dfrac{1}{48}\)+ ...+ \(\dfrac{1}{2400}\)

= \(\dfrac{1}{2\times4}\)  +\(\dfrac{1}{4\times6}\) + \(\dfrac{1}{6\times8}\) +...+ \(\dfrac{1}{48\times50}\)

= \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{2}{2\times4}\) +\(\dfrac{2}{4\times6}\)+ \(\dfrac{2}{6\times8}\) +...+ \(\dfrac{2}{48\times50}\))

= \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{1}{2}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{6}\) + \(\dfrac{1}{6}\) - \(\dfrac{1}{8}\) +...+ \(\dfrac{1}{48}\) - \(\dfrac{1}{50}\))

= \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{1}{2}\) - \(\dfrac{1}{50}\))

= \(\dfrac{1}{2}\) \(\times\) \(\dfrac{12}{25}\)

= \(\dfrac{6}{25}\)