Chebyshev and Pade

Hi
Does anyone know how many terms we are supposed to use in writing out a Chebyshev series? I know it normally will state to use the 3rd order (for example) which means using terms T0 to T3, but does that mean we do not convert any of the powers higher than x^3? The textbook expands the 3rd-order Chebyshev series further than this, but leaves out the terms higher than T4 when substituting.

For example, the textbook substitutes (1/8)(3T0 + 4T2 + T4) for x^4 and merely leaves off the T4 term. (see page 229) This can obviously go on forever because the higher powers of x still have valid terms (T0-T3) in them and the Maclaurin or Taylor series can be infinite. Where do we draw the line??

Also, does anyone have any better explanations or resources for Pade approximations?

Thanks
Rory

I don't see that in the book perhaps it is a different edition - mine is 7th.
In the exam they tell you where to stop - i.e. a Maclaurin series is given with four terms and four Chebyshev polynomials

This was very useful for me for Pade as it contains vital piece of information missing from the textbook: http://ktuce.ktu.edu.tr/~pehlivan/numerical_analysis/chap03/PadeApproximation.pdf

Thank you!
I'm dreading this one tomorrow!