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Root Test
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Re: Root test
by Guest » Mon Oct 25, 2021 5:55 pm
You titled this "Root Test". What is your understanding of the root test?
- Guest
Re: Root Test
by Guest » Sat Dec 25, 2021 9:25 pm
Since the first "guest" has not answered as to what his/her understanding of the "root test" is:
The kth root of the kth term in this is [tex]\frac{3k^2+ 5}{k^2+ 7}[/tex]. Dividing the numerator and denominator by [tex]k^2[/tex], [tex]\frac{3+ \frac{5}{k^2}}{1+ \frac{7}{k^2}}[/tex]. As k goes to infinity, that goes to [tex]\frac{3}{1}= 3[/tex]. That is larger than 1 so the series does NOT converge.
The kth root of the kth term in this is [tex]\frac{3k^2+ 5}{k^2+ 7}[/tex]. Dividing the numerator and denominator by [tex]k^2[/tex], [tex]\frac{3+ \frac{5}{k^2}}{1+ \frac{7}{k^2}}[/tex]. As k goes to infinity, that goes to [tex]\frac{3}{1}= 3[/tex]. That is larger than 1 so the series does NOT converge.
- Guest
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