Alright, I need some help with this.(adsbygoogle = window.adsbygoogle || []).push({});

a_{n}= [itex]\frac{1 - 5n^{4}}{n^{4} + 8n^{3}}[/itex]

To find the limit of convergence, use l'Hopital's Rule. The result will come out to

L = -5

From my book,

"The sequence {a_{n}} converges to the number L if for every positive number ε there corresponds an integer N such that for all n,

n > N → | a_{n}- L | < ε"

So, to check that L = -5 is true, substitute in? How do I show that L = -5 using this definition?

| a_{n}- L | < ε

| [itex]\frac{1 - 5n^{4}}{n^{4} + 8n^{3}}[/itex] - (-5) | < ε

Let n = 1, ε = 1

| [itex]\frac{1 - 5}{1 + 8}[/itex] + [itex]\frac{45}{9}[/itex]) | < ε = 1

[itex]\frac{41}{9}[/itex] < ε = 1,which is not true

Thank you for your time! This definition is very confusing to me for some reason.

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