Numerical Methods: Euler to Runge–Kutta · Challenge problem

Euler's method with $n$ steps on $y' = y$, $y(0) = 1$, over $[0, 1]$ gives $E_n = \left(1 + \dfrac{1}{n}\right)^n$ as its estimate of $e$. Find $\displaystyle\lim_{n \to \infty} n\,(e - E_n)$.