\(\dfrac{1}{7}+\dfrac{1}{14}+\dfrac{1}{28}+\dfrac{1}{56}+\dfrac{1}{112}\)
\(=\dfrac{1\times16}{7\times16}+\dfrac{1\times8}{14\times8}+\dfrac{1\times4}{28\times4}+\dfrac{1\times2}{56\times2}+\dfrac{1\times1}{112\times1}\)
\(=\dfrac{16}{112}+\dfrac{8}{112}+\dfrac{4}{112}+\dfrac{2}{112}+\dfrac{1}{112}\)
\(=\dfrac{28}{112}+\dfrac{2}{112}+\dfrac{1}{112}\)
\(=\dfrac{31}{112}\)