\frac{a_1^2}{b_1}+\frac{a_2^2}{b_2}+\cdots +\frac{a_n^2}{b_n}+\frac{a_{n+1}^2}{b_{n+1}} \ge \frac{(a_1+a_2+\dots+a_n)^2}{b_1+b_2+\dots+b_n}+\frac{a_{n+1}^2}{b_{n+1}}