Finding Taylor Series and MacLaurin Series Step by Step using the TiNspire is as easy as pie:

Say you are asked to find the Taylor Series centered at a=0 up to degree n=3 (really a MacLaurin series as the center is at 0 )

So plug into Calculus Made Easy option 7 D as follows :

The derivatives are taken in order to compute the coefficients for each term up to degree 3.

The final answer is of degree 2 as the coefficient for the 3rd degree term is 0.

Additionally, other series topics such as interval of convergence and alternating series and Lagrange errors can be found as well using Calculus Made Easy at https://tinspireapps.com/?a=cme