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## Main Question or Discussion Point

I'm sorry if this question is retarded-like but is it true that;

[tex]f:\mathbb{R} \to \mathbb{R}, \forall x \in \mathbb{R}, f(x)\geq 0 \Rightarrow \sum_{n=a}^b f(n) = O\left(\int_a^b f(x) \mathrm{d} x\right)[/tex]

?

My intuition says yes, however my mind is a tad clouded now and perhaps a short counterexample (excluding f(x)=0 please :P, edit: however if you insist i can remove the equality part of the "less than or equal") can be exhibited?

(also sorry for bad notation and/or english)

[tex]f:\mathbb{R} \to \mathbb{R}, \forall x \in \mathbb{R}, f(x)\geq 0 \Rightarrow \sum_{n=a}^b f(n) = O\left(\int_a^b f(x) \mathrm{d} x\right)[/tex]

?

My intuition says yes, however my mind is a tad clouded now and perhaps a short counterexample (excluding f(x)=0 please :P, edit: however if you insist i can remove the equality part of the "less than or equal") can be exhibited?

(also sorry for bad notation and/or english)