Why is this summation formula wrong?

Question

This is the alternate form of the summation formula: $$ \sum^{n}_{k=0} a(c)^k = \frac{ac^{n+1} - a}{c - 1} $$

so why is this wrong? $$ \sum^{n}_{k=0} (-\frac{1}{2})^k = \frac{(-\frac{1}{2})^{n+1} - 1}{(-\frac{1}{2}) - 1} $$

Answer 1

This formula is correct for $c\ne 1$.

Fraction in RHS has no sense, when $c=1$ $\Bigl($undefined value like $\dfrac{0}{0}$$\Bigr)$.