Continuous positive function such that $\int\limits_1^{\infty}f(x)dx$ converges, while $\int\limits_1^{\infty}f^2(x)dx$ diverges
Find a continuous function $f:[1,\infty)\to\Bbb R $ such that $f(x) >0 $, $\int_1^\infty f(x)\,dx $ converges and $\int_1^\infty f(x)^2\,dx$ diverges