Asymptotic bounds on geometric sums
Hints:


In the first case, use the inequalities
$$
1 \leq \sum_{i=0}^n c^i = \frac{1-c^{n+1}}{1-c} \leq \frac{1}{1-c}.
$$
In the second case, use the inequalities
$$
c^n \leq \sum_{i=0}^n c^i = \frac{c^{n+1}-1}{c-1} \leq \frac{c}{c-1} c^n.
$$