Question

A=5/4x7 + 5/7x10 + ........ + 5/25x28 + 5/28x31

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Answer 1

\(A=\dfrac{5}{4x7}+\dfrac{5}{7x10}+...+\dfrac{5}{25x28}+\dfrac{5}{28x31}\)

\(\dfrac{3}{5}A=\dfrac{7-4}{4x7}+\dfrac{10-7}{7x10}+...+\dfrac{28-25}{25x28}+\dfrac{31-28}{28x31}\)

\(\dfrac{3}{5}A=\dfrac{7}{4x7}-\dfrac{4}{4x7}+\dfrac{10}{7x10}-\dfrac{7}{7x10}+...+\dfrac{28}{25x28}-\dfrac{25}{25x28}+\dfrac{31}{28x31}-\dfrac{28}{28x31}\)

\(\dfrac{3}{5}A=\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{25}-\dfrac{1}{28}+\dfrac{1}{28}-\dfrac{1}{31}\)

\(\dfrac{3}{5}A=\dfrac{1}{4}-\dfrac{1}{31}=\dfrac{27}{124}\)

\(A=\dfrac{27}{124}:\dfrac{3}{5}=\dfrac{27}{124}x\dfrac{5}{3}=\dfrac{45}{124}\)