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Suppose f(x) is a degree 8 polynomial such that f(2^i)=1/(2^i) for all integers 0≤i≤8. If f(0)=a/b, where a and b are coprime positive integers, what is the value of a+b?
\[f(2^i)=\frac{1}{2^{i}}\]
sorry i got to go, i'll back to this later, i would be happy if i can help :)
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