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**nukenuts** Question 37 from 11.8 of Stewart's Early Transcendentals -

A function is defined by

f(x) = 1 + 2x + x^2 + 2x^3 + x^4.....

that is, its coefficients are C (2n) = 1 and C (2n+1) = 2 for all n >= 0.

Find the interval of convergence of the series and find an

explicit formula for f(x)

The answer is given at the end of the book as

Interval of convergence = (-1, 1)

f(x) = (1 + 2x)/(1 - x^2)

Anyone know how to calculate f(x) because there are no examples like this in the book. I can't even see how that value of f(x) is correct, how does f(x) relate to the given power series, how does f(x) = (1 + 2x)/(1 - x^2) = 1 + 2x + x^2 + 2x^3 + x^4.....