Showing that $\sum_{k=1}^n\dfrac{1}{2^{k-1}}$ for $n \geq 2$ is not an integer . Suppose $n\geq2 ,s(n)=\sum_{k=1}^n\dfrac{1}{2^{k-1}} $ 
$$s(2)=1+\frac 12=1.5\\s(3)=1+\frac12+\frac14=1.75 ,\\\vdots$$
Is an elementary proof to $s(n)$ can never be an integer number ?
As honestly as possible : One of my students( k-12) asked this question .I said I will think and answer .But I got stuck ...
I am thankful for your hint,guide or solutions in advanced.

$2^{n-1} s(n)$ is odd and $\frac{\text{odd}}{\text{even}\neq 0}$ cannot be an integer.
