Question

Is the following statement "Since ( lim _{n ightarrow infty}left(frac{frac{1}{n sqrt{n^{6}+3}}}{frac{1}{n^{2}}} ight)=0 ) and ( sum_{n=1}^{infty} frac{1}{n^{2}} ) is convergent, by Limit Comparison Test ( sum_{n=1}^{infty} frac{1}{n sqrt{n^{6}+3}} ) is convergent." true or false? Select one: True False

          Is the following statement
"Since ( lim _{n 
ightarrow infty}left(frac{frac{1}{n sqrt{n^{6}+3}}}{frac{1}{n^{2}}}
ight)=0 ) and ( sum_{n=1}^{infty} frac{1}{n^{2}} ) is convergent, by Limit Comparison Test ( sum_{n=1}^{infty} frac{1}{n sqrt{n^{6}+3}} ) is convergent."
true or false?
Select one:
True
False

$Is the following statement "Since ( lim n ightarrow inftyleft(fracfrac1n sqrtn^6+3frac1n^2 ight)=0 ) and ( sumn=1^infty frac1n^2 ) is convergent, by Limit Comparison Test ( sumn=1^infty frac1n sqrtn^6+3 ) is convergent." true or false? Select one: True False$

Added by Saadet Burcu T.

Calculus Single Variable

Deborah Hughes-Hallett, Andrew M.… 7th Edition

Chapter 9

Instant Answer

Solved by Expert H M

06/19/2023

Step 1

First, we need to find the limit of the given expression: $ \lim _{n \rightarrow \infty}\left(\frac{\frac{1}{n \sqrt{n^{6}+3}}}{\frac{1}{n^{2}}}\right) $ This simplifies to: $ \lim _{n \rightarrow \infty}\left(\frac{n^{2}}{n \sqrt{n^{6}+3}}\right) $ Now, we Show more…

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