Evaluate (\(\frac{1}{2} – \frac{1}{4} + \frac{1}{8} – \frac{1}{16} + …) -1\)

Explanation

S\(_{∞}\) = \(\frac{\text{a}}{(1-r)}\), where a = \(\frac{1}{2}\), r = -\(\frac{1}{2}\).

S\(_{∞}\) = \(\frac{\frac{1}{2}}{1 - \frac{-1}{2}}\)  = \(\frac{\frac{1}{2}}{\frac{3}{2}}\) = \(\frac{1}{2}\) x \(\frac{2}{3}\)
\(\frac{1}{3}\) - 1 = -\(\frac{2}{3}\)

There is an explanation video available .