I'm working on a double induction problem with the following prompt:

Prove by induction on $n$ that for any real number $q > 1$ and integer $n \ge 0$: $$ 1 + q + q^2 + q^3 + \cdots + q^{n-1} + q^n = \frac {q^{n+1}-1}{q-1} $$

Based on Induction on two integer variables, I would imagine the solution is:

- Base case $(q,n)$ as $(2,n)$ and $(q,0)$
- Assume premise for $(2,n)$ and prove $n+1$
- Assume premise for $(q,0)$ and prove $q+1$

But even the base cases confuse me...for example on $(q,0)$: $$1+q^0 = \frac {q^{0+1}-1}{q-1} $$ $$2 = 1 $$

That can't right. Maybe I omit the $q^0$ on the LHS, but why?