Give an example for a continuous function f : R ≥ 0 → R ≥ 0 {\displaystyle {}f\colon \mathbb {R} _{\geq 0}\rightarrow \mathbb {R} _{\geq 0}} and an absolutely convergent real series ∑ k = 0 ∞ a k {\displaystyle {}\sum _{k=0}^{\infty }a_{k}} with a k ≥ 0 {\displaystyle {}a_{k}\geq 0} such that the series ∑ k = 0 ∞ f ( a k ) {\displaystyle {}\sum _{k=0}^{\infty }f(a_{k})} does not converge.
