Sequence Math Example 2

Solution

1. 1
   Divide numerator and denominator by $n^2$.
2. 2
   Numerator becomes $3 + \frac{1}{n^2}$; denominator becomes $1 + \frac{2}{n^2}$.
3. 3
   As $n \to \infty$, both $\frac{1}{n^2}$ and $\frac{2}{n^2}$ approach 0.
4. 4
   $\lim_{n\to\infty} a_n = \frac{3+0}{1+0} = 3$.