This rational function

has two singularities, in x = 1 and in x = -1.

The Taylor series converges in an interval centered at the center of the series but not outside it. The radius of the interval of convergence is the distance from the center of the series to the nearest singularity.

This behavior is similar to other functions with singularities.

We can compare this behavior with that of other similar (but continuos) function.

LINKS

	Taylor polynomials: Rational function without real singularities This is a continuos function and has no real singularities. However, the Taylor series approximates the function only in an interval. To understand this behavior we should consider a complex function.
	Taylor polynomials: Rational function with two complex singularities We will see how Taylor polynomials approximate the function inside its circle of convergence.
	Taylor polynomials: Rational function 1 The function has a singularity at -1. Taylor polynomials about the origin approximates the function between -1 and 1.
	Taylor polynomials: Rational function 2 The function has a singularity at -1. Taylor polynomials about the origin approximates the function between -1 and 1.
	Taylor polynomials: Sine function By increasing the degree, Taylor polynomial approximates the sine function more and more.
	Taylor polynomials: Square root The function is not defined for values less than -1. Taylor polynomials about the origin approximates the function between -1 and 1.
	Taylor polynomials: Exponential function By increasing the degree, Taylor polynomial approximates the exponential function more and more.