Let $0.5 and let $b=1-a$. Let $n\in \mathbb{N}$.
$\left|\left(\frac{a}{b}\right)^n-\left(\frac{a}{b}\right)^{n-1}\right|\le C$.
Is $\left|\left(\frac{a}{b}\right)^n-\left(\frac{a}{b}\right)^{n-1}\right|\le C$ bounded by a constant $C$ for all $n$? If so, how would I show it/explain it?