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.....