Matematické Fórum

stuart clark · 09. 07. 2016 08:58

If $f(x)$ is a differentiable function from $\mathbb{R}\rightarrow \mathbb{Q}\;,$ Then $\sum^{100}_{r=0}(-1)^rf(r)$

vanok · 13. 07. 2016 11:11 — Editoval vanok (13. 07. 2016 11:12)

Hi,
To solve this exercise, you can use three theorems
1) Any differentiable function of one real variable is a is continuous
2) Intermediate value theorem
3) Any continuons function $f:\mathbb{R}\rightarrow \mathbb{Q}\;$ is a constant function. (Theorem 3) is deducted from the theorem 2))
Answer

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Remark, it is better to write f, for a function, and not f (x).

stuart clark · 18. 07. 2016 10:35

Thanks ↑ vanok: got it.

Matematické Fórum

#1 09. 07. 2016 08:58

summation of function

#2 13. 07. 2016 11:11 — Editoval vanok (13. 07. 2016 11:12)

Re: summation of function

#3 18. 07. 2016 10:35

Re: summation of function

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