Is there any possibility that for any positive values of $\alpha_i$ also ($\alpha_i \neq \alpha_j$), the below condition holds ?
$$ \frac{(\sum_i^k \alpha_i)^2}{\sum_i^k \alpha_i^2} < \frac{(\sum_i^l \alpha_i)^2}{\sum_i^l \alpha_i^2} $$ when $l > k$ ?