lim(n→∞)(a1+…+an)/n=a，0＜ak＜M，求证 lim(n→∞)∑(1≤i＜j≤n)aiaj/n^2=a^2/2

elim

【题】已知 \(\displaystyle\lim_{n\to\infty}\frac{a_1+\cdots+a_n}{n}=a.\;(a_k>0\;\forall k)\) 求证
\(\qquad\;\,\displaystyle\lim_{n \to \infty} \frac{\sum_{1 \le i_1< i_2<\dots< i_m \le n} a_{i_1}\dots a_{i_m}}{n^m}=\frac{a^m}{m!}\)

luyuanhong

luyuanhong

elim

谢谢陆老师的解答！