This is a geometric series (a * (r^n)) of the form .9(.1 ^ n) power. Because we can prove the convergence of geometric series (in certain instances) using the formula a / (1 - r), after plugging in the terms, we get .9 / (1 - .1) = .9/.9 = 1. Series and sequences are fun! (But screw Taylor series and polynomails, those were horrible...)
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