A Stupid(?) Question

[RocketManJames]

Sum of Geometric Series converges when C < 1. One of the proofs of this that I learned back in school follows.

So, S = C^0 + C^1 + C^2 + ...
C*S = C^1 + C^2 + C^3 + ...
S - C*S = C^0
S = C^0 / (1 - C) = 1 / (1 - C)

Now, comes the stupid question... how does this proof fail for C > 1? What is the reason why this proof is valid when C < 1 and invalid when C > 1? At C = 1, we clearly see that the answer is undefined... but at C > 1, S is equal to some negative number, which is obviously wrong. But, my question, lame as it may be, is exactly where is it that this proof becomes invalid?

Thanks.

-RMJ