Question

Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) an = 7n 1 + 8n lim n→[infinity] an = Incorrect:

Answer 1

Answer:

The sequence diverges

Step-by-step explanation:

Given the sequence:

$a_n=7n(1+8n)=7n+56n^2$

Let's use the zero test which states:

$\Sigma a_n\\Diverges\hspace{3}if\hspace{3} \lim_{n \to \infty} a_n \neq0$

So, let's find the limit:

$\lim_{n \to \infty} 7n+56n^2= \lim_{n \to \infty} 7n + \lim_{n \to \infty} 56n^2$

For the first limit:

$\lim_{n \to \infty} 7n= 7 \lim_{n \to \infty} n=7* \infty=\infty$

For the second limit:

$\lim_{n \to \infty} 56n^2=56 \lim_{n \to \infty} n^2 =56(\infty)^2=\infty$

So:

$\lim_{n \to \infty} 7n+56n^2=\infty +\infty=\infty$

Therefore, the sequence diverges