A = \(\dfrac{1}{3.5}+\dfrac{1}{5.7}+\dfrac{1}{7.9}+.....+\dfrac{1}{37.39}\)
A = \(\dfrac{1}{2}\) . ( \(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{37.39}\))
A = \(\dfrac{1}{2}\) .( \(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+......+\dfrac{1}{37}-\dfrac{1}{39}\))
A = \(\dfrac{1}{2}\).( \(\dfrac{1}{3}\) - \(\dfrac{1}{39}\))
A = \(\dfrac{1}{2}\). ( \(\dfrac{13}{39}\) - \(\dfrac{1}{39}\))
A = \(\dfrac{1}{2}\). \(\dfrac{12}{39}\)
A = \(\dfrac{2}{13}\)