Find Limit of $\frac{n^3}{(n + 1)^2}$ as $n$ Approaches ∞

[tmt1]

I need to find the limit of

$$\left| \frac{(n + 1)n^3}{(n + 1)^{3}} \right|$$

as $n$ approaches infinity.

I simplify this to:

$$\left| \frac{n^3}{(n + 1)^{2}} \right|$$

But the solution simplifies it to:

$$\left| \frac{n}{(1 + \frac{1}{n})^{2}} \right|$$

How do I get to this result?

 

[topsquark]

I need to find the limit of

$$\left| \frac{(n + 1)n^3}{(n + 1)^{3}} \right|$$

as $n$ approaches infinity.

I simplify this to:

$$\left| \frac{n^3}{(n + 1)^{2}} \right|$$

But the solution simplifies it to:

$$\left| \frac{n}{(1 + \frac{1}{n})^{2}} \right|$$

How do I get to this result?

\(\displaystyle \left | \frac{n^3}{(n + 1)^{2}} \right |\)

\(\displaystyle = \left | \frac{n^2 \cdot n}{(n + 1)^{2}} \right | = \left | \frac{n}{\frac{(n + 1)^{2}}{n^2}} \right |\)

Can you finish from here?

-Dan