A = \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) + \(\dfrac{1}{32}\)+.....+ \(\dfrac{1}{134}\)+ \(\dfrac{1}{268}\)
A \(\times\) 2 = 1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) + \(\dfrac{1}{32}\) +.....+ \(\dfrac{1}{134}\)
A \(\times\) 2 - A = 1 - \(\dfrac{1}{268}\)
A \(\times\) ( 2 - 1) = \(\dfrac{267}{268}\)
A = \(\dfrac{267}{268}\)