I want to prove that (without using Fatou's lemma)
for every $k \in N$ let $f_k$ be a nonnegative sequence $f_k(1),f_k(2),\ldots$
$\sum^\infty_{n=1}\liminf_{k \to \infty} f_k(n) \le \liminf_{k \to \infty} \sum^\infty_{n=1}f_k(n)$
Can you give some hint for me about that? hat