Question 82
Let $x \lt 0.1$ be a positive real number. Let the foury series be $4 + 4x + 4x^{2} + 4x^{3} + \ldots$, and let the fourier series be $4 + 44x + 444x^{2} + 4444x^{3} + \ldots$. Suppose that the sum of the fourier series is four times the sum of the foury series. Compute $x$.