Answer:
The sequence diverges
Step-by-step explanation:
Given the sequence:
[tex]a_n=7n(1+8n)=7n+56n^2[/tex]
Let's use the zero test which states:
[tex]\Sigma a_n\\Diverges\hspace{3}if\hspace{3} \lim_{n \to \infty} a_n \neq0[/tex]
So, let's find the limit:
[tex]\lim_{n \to \infty} 7n+56n^2= \lim_{n \to \infty} 7n + \lim_{n \to \infty} 56n^2[/tex]
For the first limit:
[tex]\lim_{n \to \infty} 7n= 7 \lim_{n \to \infty} n=7* \infty=\infty[/tex]
For the second limit:
[tex]\lim_{n \to \infty} 56n^2=56 \lim_{n \to \infty} n^2 =56(\infty)^2=\infty[/tex]
So:
[tex]\lim_{n \to \infty} 7n+56n^2=\infty +\infty=\infty[/tex]
Therefore, the sequence diverges
