Section 10.1 : Sequences
3. Determine if the given sequence converges or diverges. If it converges what is its limit?
\[\left\{ {\frac{{{n^2} - 7n + 3}}{{1 + 10n - 4{n^2}}}} \right\}_{n = 3}^\infty \]Show All Steps Hide All Steps
Start SolutionTo answer this all we need is the following limit of the sequence terms.
\[\mathop {\lim }\limits_{n \to \infty } \frac{{{n^2} - 7n + 3}}{{1 + 10n - 4{n^2}}} = - \frac{1}{4}\]You do recall how to take limits at infinity right? If not you should go back into the Calculus I material do some refreshing on limits at infinity as well at L’Hospital’s rule.
Show Step 2We can see that the limit of the terms existed and was a finite number and so we know that the sequence converges and its limit is \( - \frac{1}{4}\).