Question

Tính

\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}\)

Answer 1

\(\frac{1}{2}+\frac{5}{6}+...+\frac{55}{56}\)

\(=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+...+\left(1-\frac{1}{56}\right)\)

\(=7.1-\left(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{56}\right)\)

\(=7-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{7.8}\right)\)

\(=7-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{7}-\frac{1}{8}\right)\)

\(=7-\left(1-\frac{1}{8}\right)\)

\(=7-\frac{7}{8}=\frac{49}{8}\)

Answer 2

\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}=\frac{1889}{312}\)