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)(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)(3n^5)/(6n^6+1)=\lim _(n\to\infty)(3n^5)/(6n^6)=(1)/(2)\lim _(n\to\infty)\frac{1^{}}{n^{}}=0`

The limit of this serie is equal to zero.