Sum of Geometric Sequence/Examples/Index to Minus 2

Theorem
Let $x$ be an element of one of the standard number fields: $\Q, \R, \C$ such that $x \ne 1$.

Then the formula for Sum of Geometric Progression:
 * $\displaystyle \sum_{j \mathop = 0}^n x^j = \frac {x^{n + 1} - 1} {x - 1}$

breaks down when $n = -2$:
 * $\displaystyle \sum_{j \mathop = 0}^{-2} x^j \ne \frac {x^{-1} - 1} {x - 1}$

Proof
The summation on the is vacuous:
 * $\displaystyle \sum_{j \mathop = 0}^{-2} x^j = 0$

while on the we have: