Question

I need help solving thisI’m struggling It’s from my ACT prep-guide.

Answer 1

The limit of a series is the value the series' terms are approaching as n goes to infinity.

We want to calculate

$\lim _{n\to\infty}\frac{3n^5}{6n^6+1}$

As n goes to infinity, the behavior of the denominator can be approximated in a way ignoring the constant

$n\rightarrow\infty\Rightarrow6n^6+1\approx6n^6$

Using this approximation in our limit, we have

$\lim _{n\to\infty}\frac{3n^5}{6n^6+1}=\lim _{n\to\infty}\frac{3n^5}{6n^6}=\frac{1}{2}\lim _{n\to\infty}\frac{1^{}}{n^{}}=0$

The limit of this serie is equal to zero.