Question: A function f is defined by f(x) = 1 + 2x + x2 + 2x3 + x4 + ... that is, its coefficients are c2n

A function f is defined by
f(x) = 1 + 2x + x2 + 2x3 + x4 + ...
that is, its coefficients are c2n = 1 and c2n+1 = 2 for all n ( 0. Find the interval of convergence of the series and find an explicit formula for f(x).

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