Ta có:
\(\dfrac{1}{20}=\dfrac{1}{4}-\dfrac{1}{5}\)
\(\dfrac{1}{14}=\dfrac{1}{10}-\dfrac{1}{35}\)
\(\dfrac{1}{56}=\dfrac{1}{7}-\dfrac{1}{8}\)
Thay vào ta được:
\(2 + \dfrac{1}{4}+ \dfrac{3}{4} - \dfrac{3}{5}+\dfrac{1}{10} + \dfrac{1}{10} - \dfrac{1}{35}+ \dfrac{3}{7} - \dfrac{3}{8} + \dfrac{1}{24} \)
\(= 3 - \dfrac{2}{5} - \dfrac{1}{35} + \dfrac{3}{7} - \dfrac{3}{8}+ \dfrac{1}{24} \)
\(= 3 + \dfrac{1}{35} - \dfrac{1}{35} + \dfrac{1}{24} - \dfrac{3}{8} \)
\(= 3 + \dfrac{1}{24} - \dfrac{3}{8}\)
\(= 2 + \dfrac{5}{8}+ \dfrac{1}{24} \)
\(= 2 + \dfrac{1}{8} (5 + \dfrac{1}{3}) \)
\(= 2 + \dfrac{16}{24} \)
\(=2+\dfrac{2}{3}\)
\(=\dfrac{8}{3}\)
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