Question

 A= \(\dfrac{7}{3x6}\)  + \(\dfrac{7}{6x9}\)  + \(\dfrac{7}{9x12}\)  + \(\dfrac{7}{12x15}\)  + ... + \(\dfrac{7}{96x99}\)                                                                                                        

                                                                                                                   

Answer 1

A = \(\dfrac{7}{3\times6}\) + \(\dfrac{7}{6\times9}\) + \(\dfrac{7}{9\times12}\) + \(\dfrac{7}{12\times15}\)+ .....+\(\dfrac{7}{96\times99}\)

A = \(\dfrac{7}{3}\) x ( \(\dfrac{3}{3\times6}\) + \(\dfrac{3}{6\times9}\)+ \(\dfrac{3}{9\times12}\)+ \(\dfrac{3}{12\times15}\)+......+\(\dfrac{3}{96\times99}\))

A = \(\dfrac{7}{3}\) x ( \(\dfrac{1}{3}\) - \(\dfrac{1}{6}\) + \(\dfrac{1}{6}\) - \(\dfrac{1}{9}\) + \(\dfrac{1}{9}\) - \(\dfrac{1}{12}\)+ \(\dfrac{1}{12}\) - \(\dfrac{1}{15}\)+....+ \(\dfrac{1}{96}\) - \(\dfrac{1}{99}\))

A = \(\dfrac{7}{3}\) x ( \(\dfrac{1}{3}\)- \(\dfrac{1}{99}\))

A = \(\dfrac{224}{297}\)