Why is it impossible to expand (x) = |x| as a power series that converges in an interval around x = 0? Explain using Theorem

Why is it impossible to expand ƒ(x) = |x| as a power series that converges in an interval around x = 0? Explain using Theorem 2.

THEOREM 2 Term-by-Term Differentiation and Integration Assume that F(x) = an(x-c)" n=0 has radius of convergence R > 0. Then F is differentiable on (c- R,c + R). Further- more, we can integrate and differentiate term by term. For x = (c - R,c + R), F'(x) = nan(x-c)"-1 [F(x) d. n=1 F(x) dx = A + 8 an n+1 -(x = c)"+1 (A any constant) n=0 For both the derivative series and the integral series the radius of convergence is also R.