M = \(\dfrac{5}{2.4}\) + \(\dfrac{5}{4.6}\)+ \(\dfrac{5}{6.8}\)+ ...+ \(\dfrac{5}{96.98}\)+ \(\dfrac{5}{98.100}\)
M = \(\dfrac{5}{2}\).( \(\dfrac{2}{2.4}\) + \(\dfrac{2}{4.6}\)+ \(\dfrac{2}{6.8}\)+...+ \(\dfrac{2}{96.98}\)+ \(\dfrac{2}{98.100}\))
M = \(\dfrac{5}{2}\).( \(\dfrac{1}{2}-\dfrac{1}{4}\)+ \(\dfrac{1}{4}-\dfrac{1}{6}\)+ \(\dfrac{1}{6}\) - \(\dfrac{1}{8}\)+...+ \(\dfrac{1}{96}\)-\(\dfrac{1}{98}\)+ \(\dfrac{1}{98}\)-\(\dfrac{1}{100}\))
M = \(\dfrac{5}{2}\).(\(\dfrac{1}{2}\) - \(\dfrac{1}{100}\))
M = \(\dfrac{49}{40}\)
\(x\) \(\times\) M - 1 = \(\dfrac{20}{29}\)
\(x\) \(\times\) \(\dfrac{49}{40}\) = \(\dfrac{20}{29}\) + 1
\(x\) \(\times\) \(\dfrac{49}{40}\) = \(\dfrac{49}{29}\)
\(x\) = \(\dfrac{49}{29}\) : \(\dfrac{49}{40}\)
\(x\) = \(\dfrac{40}{29}\)
