Continuous function/No series criterion/Exercise

Give an example for a continuous function ${}f\colon \mathbb {R} _{\geq 0}\rightarrow \mathbb {R} _{\geq 0}$ and an absolutely convergent real series ${}\sum _{k=0}^{\infty }a_{k}$ with ${}a_{k}\geq 0$

such that the series ${}\sum _{k=0}^{\infty }f(a_{k})$ does not converge.

Create a solution