I have a quadratic based sequence, say its of the general form : $y = ax^2 + bx +c$
To put a concrete example the sequence : $a(n) = n^2 +5n +6$
$\lim{a(n)}\to\infty$ when $n\to\infty$
I am trying to think of an Epsilon-N way to prove this. I am not sure how to start to break down the quadratic, would one factor it in product form and manipulate that, or would one use some kind of Triangle Inequality on the quadratic.
Hope to get some clarification on this.
We notice that for positive $n$ we have $$a(n)> n^2$$Now for each $M$ we can choose $N=\max\{|M|,1\}$ and thus for $n>N$ we get $$a(n)>n^2\ge N^2\ge |M|^2\ge |M|\ge M$$