Answer
converges to $5$
Work Step by Step
To determine if a sequence converges, see if the limit as $n$ approaches infinity exists.
$\lim\limits_{n \to \infty}\frac{10n^{2}+3n+7}{2n^{2}-6}$
To find the limit as $n$ approaches infinity for two polynomial functions in numerator and denominator, determine the highest degree of each expression. The highest degree (2nd degree) is the same, so the limit as $n$ approaches infinity is simply the quotient of the highest degree polynomial's coefficients.
$=\frac{10}{2}=5$
Therefore, the sequence converges to $5$.
