$($a$)$ Device a method to represent a number $(b^n-1)$ as a base $b$ number, where $b$ can be any integer larger than $1$ and $n$ any integer larger than $0.$ Give a mathematical derivation of your result. Using this method convert $(5^2-1)$ and $(5^3-1)$ as base $5$ numbers.

$($CO$1)$

Answer me correctly with proper explanation $,$ otherwise i will downvote!