let Σ f_n (x) with f_n (x) = ((sin(nx))/(n^2 (n+1))) and S its sum x∈[−π,π] prove that ∀(x,y)∈[−π,π]^2 x≠y ⇒∣S(x)−S(y)∣<∣x−y∣ .


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Question Number 33701 by math khazana by abdo last updated on 22/Apr/18

$l e t Σ f_{n} (x) w i t h f_{n} (x) = \frac{s i n (n x)}{n^{2} (n + 1)} a n d S i t s s u m$ $x \in [- π, π] p r o v e t h a t \forall (x, y) \in {[- π, π]}^{2}$ $x \neq y \Rightarrow∣ S (x) - S (y) ∣<∣ x - y ∣ .$
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