What is the operation between row 2 and row 3 in the convergence of this series?

[kapitan90]

Homework Statement

I need to examine convergence of series with a term Un given below.

The solution is given, but I can't understand what happens between row 2 and row 3.
What kind of operation is that, does it have something in common with Taylor series expansion?
[PLAIN]http://img805.imageshack.us/img805/4619/convergence.png

 

[praharmitra]

It is exactly the taylor series expansion of \left(1+\frac{1}{n^3}\right)^{1/3}

 

[kapitan90]

Ok, thanks!

 

[praharmitra]

BTW, you don't need to know it by heart. You expand it using the Taylor Expansion formulas for fractional powers.