Let $X_1, X_2, \ldots $ be independent identically distributed random variables with $ E\left | X_i \right |<\infty$. Show that
$E(X_1\mid S_n,S_{n+1},\ldots)=\dfrac{S_n}{n}$ (a.s.),
where $S_n=X_1+\cdots+ X_n$
Let $X_1, X_2, \ldots $ be independent identically distributed random variables with $ E\left | X_i \right |<\infty$. Show that
$E(X_1\mid S_n,S_{n+1},\ldots)=\dfrac{S_n}{n}$ (a.s.),
where $S_n=X_1+\cdots+ X_n$