Problem

Source: III International Festival of Young Mathematicians Sozopol 2012, Theme for 10-12 grade

Tags: algebra, binomial sum, Sum, Calculate



Calculate the sum $1+\frac{\binom{2}{1}}{8}+\frac{\binom{4}{2}}{8^2}+\frac{\binom{6}{3}}{8^3}+...+\frac{\binom{2n}{n}}{8^n}+...$