## Limits with parameters

$$\displaystyle \lim_{n\to\infty}a^n$$, where $$a>0$$ is a given real number.
$$\displaystyle \lim_{n\to\infty}\frac{1+a+a^2+…+a^n}{1+b+b^2+…+b^n},$$ where $$0<a<1$$ and $$0<b<1$$ are given real numbers.