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Question Number 78447 by arkanmath7@gmail.com last updated on 17/Jan/20

prove that the seq a_n  = ((ncos(3n^2 +2n+1))/(n+1))  has convergent subsequence

$${prove}\:{that}\:{the}\:{seq}\:{a}_{{n}} \:=\:\frac{{ncos}\left(\mathrm{3}{n}^{\mathrm{2}} +\mathrm{2}{n}+\mathrm{1}\right)}{{n}+\mathrm{1}} \\ $$$${has}\:{convergent}\:{subsequence} \\ $$

Answered by mind is power last updated on 17/Jan/20

∣a_n ∣<1⇒by Weirstrass a_n  has  a[convergent Subsquence

$$\mid\mathrm{a}_{\mathrm{n}} \mid<\mathrm{1}\Rightarrow\mathrm{by}\:\mathrm{Weirstrass}\:\mathrm{a}_{\mathrm{n}} \:\mathrm{has}\:\:\mathrm{a}\left[\mathrm{convergent}\:\mathrm{Subsquence}\right. \\ $$

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