Numerical Methods: Euler to Runge–Kutta · Superchallenge problem

The problem $y' = y^2$, $y(0) = \dfrac{1}{2}$ has exact solution $y = \dfrac{1}{2 - t}$, so $y(1) = 1$. Euler's method with $n$ equal steps on $[0, 1]$ gives an estimate $Y_n$. Find $\displaystyle\lim_{n \to \infty} n\,(1 - Y_n)$.