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How would you find the Taylor series expansion of:

$f(x) = \dfrac 3{2x -1} , \text{ at}\, a = 2$

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1 Answer 1

If $x=2+z$ and $|z|\lt\frac32$, then $$ f(x)=(1+\tfrac23z)^{-1}=\sum_{n\geqslant0}(-1)^n\left(\tfrac23z\right)^n=\sum_{n\geqslant0}(-1)^n\left(\tfrac23\right)^n(x-2)^n. $$

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