- #1
roam
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Homework Statement
Prove that the sequence [tex](\frac{1}{1+n+n^4})[/tex] converges to 0.
Homework Equations
The Attempt at a Solution
Given [tex]\epsilon >0[/tex], we can find [tex]n \geq N[/tex] such that:
[tex]| \frac{1}{1+n+n^4} -0 | = \frac{1}{1+n+n^4} < \frac{1}{1+n}< \epsilon[/tex]
Now what value of N should we take to complete the proof? And why?
This is what I guess:
We have [tex]\frac{1}{1+n}< \epsilon[/tex] so,
[tex]n+1> \frac{1}{\epsilon}[/tex]
[tex]n>\frac{1}{\epsilon} -1[/tex]
[tex]N = \frac{1}{\epsilon} -1[/tex]
Is this right? I appreciate it if anyone could provide me with some explanation.