Question

Answer 1

a: \(=\left(\dfrac{75}{125}+\dfrac{2}{5}\right)+\left(\dfrac{17}{21}+\dfrac{4}{21}\right)+\left(\dfrac{15}{32}+\dfrac{17}{32}\right)=1+1+1=3\)

b: \(=\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+\dfrac{2}{3\cdot7}+\dfrac{2}{5\cdot7}+\dfrac{2}{7\cdot9}\)

\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{2}{21}\)

\(=\dfrac{8}{9}+\dfrac{2}{21}=\dfrac{62}{63}\)

c: \(=\left(\dfrac{1}{3}-\dfrac{1}{9}\right)+\left(\dfrac{1}{7}-\dfrac{1}{63}\right)=\dfrac{2}{9}+\dfrac{8}{63}=\dfrac{14+8}{63}=\dfrac{22}{63}\)