Respuesta :

[tex]\dfrac4{x+2}=\dfrac2{1-\left(-\frac x2\right)}=2\displaystyle\sum_{n\ge0}\left(-\frac x2\right)^n[/tex]

which is valid for [tex]\left|-\dfrac x2\right|<1[/tex], or [tex]|x|<2[/tex].