- #1
Askhwhelp
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ϵ-N definition of limit
Use the ϵ-N definition of limit to prove that lim[(2n+1)/(5n-2)] = 2/5 as n goes to infinity.
The way I do it is Let ∊ > 0 be given. Notice N ∈ natural number (N) which satisfies {fill this box later}< N. It follows that if n>=N, then n > {fill this box later}, so for such n, |(2n+1)/(5n-2)-2/5| = |9/(25n-10)| = 9/5|1/(5n-2)|
I am supposed to get to a something that is less than ∊
How to make this to less than ∊?
Use the ϵ-N definition of limit to prove that lim[(2n+1)/(5n-2)] = 2/5 as n goes to infinity.
The way I do it is Let ∊ > 0 be given. Notice N ∈ natural number (N) which satisfies {fill this box later}< N. It follows that if n>=N, then n > {fill this box later}, so for such n, |(2n+1)/(5n-2)-2/5| = |9/(25n-10)| = 9/5|1/(5n-2)|
I am supposed to get to a something that is less than ∊
How to make this to less than ∊?