A = \(\frac{40}{31\cdot39}+\frac{35}{39\cdot46}+\frac{30}{46\cdot52}+\frac{25}{52\cdot57}\)
A= \(5.\left(\frac{8}{31\cdot39}+\frac{7}{39\cdot46}+\frac{6}{46\cdot52}+\frac{5}{52\cdot57}\right)\)
A= \(5\cdot\left(\frac{1}{31}-\frac{1}{39}+\frac{1}{39}-\frac{1}{46}+\frac{1}{46}-\frac{1}{52}+\frac{1}{52}-\frac{1}{57}\right)\)
A= \(5.\left(\frac{1}{31}-\frac{1}{57}\right)\)
A= \(5.\left(\frac{26}{1767}\right)\)
A = \(\frac{130}{1767}\)