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## Main Question or Discussion Point

If a sequence {[tex]x_{n}[/tex]} is constant i.e [tex]\ x_{n}=c[/tex] for all nεN how can we prove [tex]limx_{n}[/tex]= c as x goes to infinity??

- Thread starter poutsos.A
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- #1

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If a sequence {[tex]x_{n}[/tex]} is constant i.e [tex]\ x_{n}=c[/tex] for all nεN how can we prove [tex]limx_{n}[/tex]= c as x goes to infinity??

- #2

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- #3

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[tex] lim\ x_{n} = c[/tex] iff for all ε>0 there exists a k belonging to the natural Nos N SUCH that :

[tex]|\ x_{n}-c|<\epsilon[/tex] ,for all n[tex]\geq[/tex] k

- #4

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Ok so pick k=1 for all epsilon.

[tex] lim\ x_{n} = c[/tex] iff for all ε>0 there exists a k belonging to the natural Nos N SUCH that :

[tex]|\ x_{n}-c|<\epsilon[/tex] ,for all n[tex]\geq[/tex] k

- #5

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