- #1
Santa1
- 111
- 0
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)