Your question is ill-posed. Is there a particular formula (e.g., \sum_{i=0}^{n-1} a r^i = a(1-r^n)/(1-r)) that you're trying to prove?
If so, this page may be some help:
http://www.mathalino.com/reviewer/derivation-of-formulas/sum-of-finite-and-infinite-geometric-progression
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Theorems is what is proven with the geometric proof.
postulates
True
Postulate, Corollary, Definition, & Theorem
Yo could try using logic.