Question 9

If $2y = \dfrac{1}{2^2} + \dfrac{1\cdot 3}{2!}\cdot \dfrac{1}{2^4} + \dfrac{1\cdot 3\cdot 5}{3!}\cdot \dfrac{1}{2^6} + \cdots$, prove that $4y^2 + 4y - 1 = 0$.