Question

Answer 1

\(A=\dfrac{20}{35\cdot31}+\dfrac{30}{35\cdot41}+\dfrac{45}{50\cdot41}+\dfrac{35}{50\cdot57}\)

\(=5\left(\dfrac{4}{31\cdot35}+\dfrac{6}{35\cdot41}+\dfrac{9}{41\cdot50}+\dfrac{7}{50\cdot57}\right)\)

=5(1/31-1/35+1/35-1/41+1/41-1/50+1/50-1/57)

=5(1/31-1/57)

\(B=\dfrac{14}{38\cdot31}+\dfrac{10}{38\cdot43}+\dfrac{6}{43\cdot46}+\dfrac{22}{46\cdot57}\)

\(=2\left(\dfrac{7}{31\cdot38}+\dfrac{5}{38\cdot43}+\dfrac{3}{43\cdot46}+\dfrac{11}{46\cdot57}\right)\)

=2(1/31-1/38+1/38-1/43+1/43-1/46+1/46-1/57)

=2(1/31-1/57)

=>A/B=5/2