Let $M_n(f(t); x) = \frac{1}{n^n} \sum_{k=0}^{\infty} d_{n,k}(x) f(\frac{k}{n})$, $x \in [0, \infty)$ \\
\text{is L.P.o, } d_{n,k}(x) = \frac{(n+k+1)!}{k!(n-1)!} x^k (1+x)^{-n-k-2} \\
\text{then } M_n(t; x) = x + \frac{2x}{n} + \frac{3x}{n^2} \\
\text{True} \\
\text{False}