⇒2S = 2 + 1 + $\frac{1}{2}$ + $\frac{1}{2²}$ +...+ $\frac{1}{2^{98}}$ + $\frac{1}{2^{99}}$
⇒2S - S = ( 2 + 1 + $\frac{1}{2}$ + $\frac{1}{2²}$ +...+ $\frac{1}{2^{98}}$ + $\frac{1}{2^{99}}$ ) + ( 1 + $\frac{1}{2}$ + $\frac{1}{2²}$ +...+ $\frac{1}{2^{99}}$ + $\frac{1}{2^{100}}$)
⇒S = 2 - $\frac{1}{2^{100}}$