Kết quả của biểu thức: \(\Large{\dfrac{11}{12}+\dfrac{19}{20}+\dfrac{2

Kết quả của biểu thức:

\(\Large{\dfrac{11}{12}+\dfrac{19}{20}+\dfrac{29}{30}+\dfrac{41}{42}+\dfrac{55}{56}+\dfrac{71}{72}+\dfrac{89}{90}+\dfrac{109}{110}}\) là:

 

• A.

  \(\Large \dfrac{257}{33}\)

• B.

  \(\Large \dfrac{256}{33}\)

• C.

  \(\Large \dfrac{256}{43}\)

• D.

  \(\Large \dfrac{556}{43}\)

\(\Large =(1 - \dfrac{1}{12})+(1 - \dfrac{1}{20})+(1 - \dfrac{1}{30})+(1 - \dfrac{1}{42})+(1 - \dfrac{1}{56})+(1 - \dfrac{1}{72})+(1 - \dfrac{1}{90})+(1 - \dfrac{1}{110})\)

\(\Large =(1+1+1+1+1+1+1+1)-(\dfrac{1}{12}+\dfrac{1}{20}+ \dfrac{1}{30}+ \dfrac{1}{42}+ \dfrac{1}{56}+ \dfrac{1}{72}+ \dfrac{1}{90}+\dfrac{1}{110})\)

\(\Large =8-(\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+ \dfrac{1}{5\times6}+ \dfrac{1}{6\times7}+ \dfrac{1}{7\times8}+ \dfrac{1}{8\times9}+ \dfrac{1}{9\times10}+\dfrac{1}{10\times11})\)

\(\Large =8-(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+ \dfrac{1}{5}-\dfrac{1}{6}+ \dfrac{1}{6}-\dfrac{1}{7}+ \dfrac{1}{7}-\dfrac{1}{8}+ \dfrac{1}{8}-\dfrac{1}{9}+ \dfrac{1}{9}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{11})\)

\(\Large =8-(\dfrac{1}{3}-\dfrac{1}{11})\)

\(\Large =8-(\dfrac{11}{33}-\dfrac{3}{33})\)

\(\Large =8-\dfrac{8}{33}\)

\(\Large =\dfrac{8\times33}{33}-\dfrac{8}{33}\)

\(\Large =\dfrac{8\times32}{33}\)

\(\Large = \dfrac{256}{33}\)