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Rudik [331]
2 years ago
7

Which statement describes the sequence defined by a Subscript n Baseline = StartFraction n cubed minus n Over n squared + 5 n En

dFraction?
Mathematics
2 answers:
Dominik [7]2 years ago
7 0

Answer:

The answer is " The sequence converges to infinity. "

Step-by-step explanation:

Given:

\to a_n=\frac{n^3-n}{n^2+5n}

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

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

Denominator= \lim_{n \to \infty} 1+\frac{5}{n}=1+\lim_{n\to \infty} \frac{5}{n}=1+0=1

Numerator =\lim_{n\to \infty}n-\frac{1}{n}=\infty

\therefore\\\\\lim_{n\to \infty}a_n=\frac{\infty}{1} =\infty

faltersainse [42]2 years ago
3 0

Answer:

converges to infinity

Step-by-step explanation:

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