General term in a sequence is a_{n}=4n+8/(n+5)
What is the sum of greatest lower bound of the sequence and lowest upper bound f the sequence. I got the answer as 5 but it must be 6.
$\displaystyle \displaystyle \begin{align*} \lim_{n \to \infty} \frac{4n + 8}{n + 5} &= \lim_{n \to \infty} \frac{4n + 20 - 12}{n + 5} \\ &= \lim_{n \to \infty} \left[ \frac{4(n + 5)}{n + 5} - \frac{12}{n + 5} \right] \\ &= \lim_{n \to \infty} \left( 4 - \frac{12}{n + 5} \right) \\ &= 4 - 0 \\ &= 4 \end{align*}$
So the least upper bound is 4.