The sum of an infinite geometric series is a remarkable thing... it can be used to prove that 0.99999... (9s forever) is exactly equal to 1.
Given 0.99999... = 0.9 + .09 + .009 + ...
The sum of an infinite geometric&series is defined as sum = t/(1-r), where t is the first term and r is the ratio between terms. Therefore:
1 = 0.9/(1-0.1)
If you don't believe it, ask your math prof.