If

$$y = \frac{1}{2(1!)}\left(\frac{1}{6}\right) + \frac{1.3}{4(2!)}\left(\frac{1}{6}\right)^2 + \frac{1.3.5}{8(3!)}\left(\frac{1}{6}\right)^3 + \dots$$

then verify that $5y^2 + 10y - 1 = 0$.