a = 1, r =$\dfrac{\left(\dfrac{1}{2}\right)}{1} $= $\dfrac{1}{2}$, n = 5

Here r < 1. Hence,

$S_6$ = $ \dfrac{a(1 - r^n)}{1 - r} $= $ \dfrac{1\left[1 - \left(\dfrac{1}{2}\right)^5 \right]}{\left(1 - \dfrac{1}{2}\right)} $

= $\dfrac{\left(1 - \dfrac{1}{32} \right)}{\left(\dfrac{1}{2}\right)}$ = $\dfrac{\left(\dfrac{31}{32}\right) }{\left(\dfrac{1}{2}\right)} $=$ \dfrac{31}{16}$ = $1\dfrac{15}{16}$