$A=\dfrac{1}{150} + \dfrac{1}{300} + \dfrac{1}{500} + \dfrac{1}{750} + \dfrac{1}{1050}$
$⇔ A= \dfrac{1}{10.15} + \dfrac{1}{15.20} + \dfrac{1}{20.25} + \dfrac{1}{25.30} + \dfrac{1}{30.35}$
$⇔ 5A= \dfrac{5}{10.15} + \dfrac{5}{15.20} + \dfrac{5}{20.25} + \dfrac{5}{25.30} + \dfrac{5}{30.35}$
$⇔ 5A = \dfrac{1}{10} - \dfrac{1}{15} + \dfrac{1}{15} - \dfrac{1}{20} + \dfrac{1}{20} - \dfrac{1}{25} + \dfrac{1}{25} - \dfrac{1}{30} + \dfrac{1}{30} - \dfrac{1}{35}$
$⇔ 5A = \dfrac{1}{10} - \dfrac{1}{35}$
$⇔ 5A = \dfrac{1}{14}$
$⇔ A = \dfrac{\dfrac{1}{14}}{5}$
