Maclaurin series for $\frac{1}{|1+x|}$

However, would it be appropriate for me to refer $\frac{1}{|1+x|}$ as 'not a smooth' curve (discontinuity at $x=1$) hence the non-existence of a Maclaurin or in any case a Taylor Series?

However, would it be appropriate for me to refer $\frac{1}{|1+x|}$ as 'not a smooth' curve (discontinuity at $x=1$) hence the non-existence of a Maclaurin or in any case a Taylor Series?