KöMaL 2006 A391

Construct a sequence $a_1$,$a_2$,...,$a_N$ of positive reals such that $n_1 a_{n0}$ +$n_2 a_{n1}$ +...+$n_k a_{nk-1}$ >2.7($a_1$+$a_2$+...+$a_N$) for arbitrary integers 1=$n_0$<$n_1$<...<$n_k$=$N$.