Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 215 / 1 / b / Solution

On the diagonal,so every summand is nonnegative. Let $m=\lceil t_{\mathrm{rel}}\rceil$. For every $i\ge 2$,HenceMultiply by $\pi (x)f_i(x{)}^2$ and sum over $i\ge 2$ to obtain the required inequality.