\(A=\dfrac{30}{4x7}+\dfrac{30}{7x10}+\dfrac{30}{10x13}+...+\dfrac{30}{37x40}\)
\(=10x\left(\dfrac{1}{4}-\dfrac{1}{7}\right)+10x\left(\dfrac{1}{7}-\dfrac{1}{10}\right)+...+10x\left(\dfrac{1}{37}-\dfrac{1}{40}\right)\)
=10x\(\left(\dfrac{1}{4}-\dfrac{1}{40}\right)=\dfrac{10x9}{10x4}=\dfrac{9}{4}\)