How would you find the Taylor series expansion of:
$f(x) = \dfrac 3{2x -1} , \text{ at}\, a = 2$
How would you find the Taylor series expansion of:
$f(x) = \dfrac 3{2x -1} , \text{ at}\, a = 2$
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. $