Question

Which statement describes the sequence defined by

Answer 1

Answer:

a) The given sequence is diverges      

$\lim_{n \to \infty} a_n$  =  ∞  

Step-by-step explanation:

Explanation

Given that the $n^{th}$ term sequence

$a_{n} = \frac{n^{3} - n}{n^{2} + 5 n}$

we have to prove that a given sequence  converges or diverges

$\lim_{n \to \infty}a_{n} = \lim_{n \to \infty} \frac{n^{3} - n}{n^{2} + 5 n}$

                  $= \lim_{n \to \infty} \frac{n^{3}(1- \frac{1}{n^{3} }) }{n^{2}(1+ \frac{5n}{n^{2} } )}$

                  $= \lim_{n \to \infty} \frac{n(1- \frac{1}{n^{3} }) }{(1+ \frac{5n}{n^{2} } )}$

                 = ∞

 $\lim_{n \to \infty} a_n$  =  ∞        

The given sequence is diverges      

Answer 2

Answer:

it is A

Step-by-step explanation:

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