Let $f : [ 1 , \infty ) \longrightarrow \mathbb { R } \backslash \{ 0 \}$ be uniformly continuous. Show that the series $\sum _ { n \geq 1 } 1 / f ( n )$ is divergent.
Let $f : [ 1 , \infty ) \longrightarrow \mathbb { R } \backslash \{ 0 \}$ be uniformly continuous. Show that the series $\sum _ { n \geq 1 } 1 / f ( n )$ is divergent.