## Calculus, 10th Edition (Anton)

first five terms: $\frac{1}{3}, \frac{1}{2}, \frac{3}{5}, \frac{2}{3}, \frac{5}{7}$, converges to 1
To find the first five terms of the sequence, put the values $1,2,3,4,5$ into the function $a_n=\frac{n}{n+2}$. To find if the sequence converges, find the limit as n approaches positive infinity. This leaves $$\lim\limits_{n \to \infty} \frac{n}{n+2}$$ Since the highest degree polynomial in the numerator and denominator match, the coefficients of those highest degree polynomials is the limit. In this case, it is $\frac{1}{1}=1$.