Numerical Methods: Euler to Runge–Kutta · Hard problem

Euler's method with $n$ equal steps on $y' = y$, $y(0) = 1$, over $[0, 1]$ produces the estimate $\left(1 + \dfrac{1}{n}\right)^n$ for $y(1) = e$. What is the smallest $n$ for which the error $e - \left(1 + \dfrac{1}{n}\right)^n$ is at most $0.05$?