Question: how to calculate the taylor series when unknown how long it is

use taylor function need to specify its limit

if we do not know its limit, 

how to know whether a function is finite in taylor expression

for example poincare series

1/((1+x)*(1+x^2))

how to display as taylor series without specify the limit of degree

because do not want to approximate poincare series with taylor 

want a complete taylor series

goal is to find the polynomials which degree are 1 and 2 in above example

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