469.Half the Sum, Exactly

Let $X_1, \dots, X_{40}$ be IID positive random variables with $E[X_1] = 2$ and $E\left[\frac{1}{X_1}\right] = 1$. Define $S_n = X_1 + \cdots + X_n$. Compute $E\left[\frac{S_{20}}{S_{40}}\right]$.