Which base of numerical system have $\frac 15 = 0.33333\ldots$? Which base of numerical system have $\frac{1}{5} = 0.33333\ldots$?
I need assistance in solving this one. 

If we are working in base $b$ (we must have $b\gt3$), then $0.3333\ldots$ is
$$0.3333\ldots = \frac{3}{b} + \frac{3}{b^2} + \frac{3}{b^3}+\cdots$$
Since
$$\sum_{n=1}^{\infty}\frac{3}{b^n} = \frac{3}{b}\sum_{n=0}^{\infty}\frac{1}{b^n} = \frac{3}{b}\left(\frac{1}{1-\frac{1}{b}}\right) =\frac{3}{b-1},$$
then...
