# How much can Titu's Lemma handle?

Algebra Level 3

Which of the following is the domain of $$(a_1,a_2,…,a_n )$$ and $$(b_1,b_2,…,b_n )$$, such that we will always have

$\frac{a_1^2}{b_1}+\frac{a_2^2}{b_2}+...+\frac{a_n^2}{b_n}\geq\frac{(a_1+a_2+...+a_n)^2}{b_1+b_2+...+b_n}$