Find the power series expansion for f(x)= 4/(x+2); x doesn't equal 2, centered at 0

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Julianaa033 Julianaa033

09-05-2017
Mathematics

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Find the power series expansion for f(x)= 4/(x+2); x doesn't equal 2, centered at 0

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LammettHash LammettHash · Answer 1 · 2017-05-09T17:00:22+02:00

LammettHash LammettHash

09-05-2017

[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].

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