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If k = frac{1}{1+2x}, where x is an integer greater than 1 and k can be represented as a terminating decimal, find the sum of all possible values of k.

May 31, 2018

Terminating decimal values for k occur when 1+2x is a power of 5, so: $$\sum k=\sum_{p=1}^\infty 5^{-p}=\frac{1}{4}$$