Question

$1,\frac{1}{2},\frac{1}{2^2},\frac{1}{2^3},$ .......... Find $S_6$.

• A. $\frac{63}{64}$
• B. $-\frac{63}{64}$
• C. $\frac{63}{32}$
• D. None of these

Answer 1

The correct option is C $\frac{63}{32}$

Clearly, the given GP has first term $a=1$ and common ratio $r=\frac{1}{2}$.
$\therefore S_6=a\times \left(\frac{r^6-1}{r-1}\right)=1\times \left(\frac{(\frac{1}{2}{)}^6-1}{\frac{1}{2}-1}\right)$
=$2\times (1-\frac{1}{2^6})$

=$2\times \left(\frac{2^6-1}{2^6}\right)$

=$2\times \left(\frac{63}{64}\right)$

=$\frac{63}{32}$