Taylor series for $\sqrt{x}$? I'm trying to figure Taylor series for $\sqrt{x}$. Unfortunately all web pages and books show examples for $\sqrt{x+1}$. Is there any particular reason no one shows Taylor series for exactly $\sqrt{x}$?

if
$$
\sqrt{x}=a_0+a_1x+a_2x^2+\dots
$$
then
$$
x=a_0^2+(a_0a_1+a_1a_0)x+(a_0a_2+a_1a_1+a_2a_0)x^2+\dots
$$
and if you want the identity theorem to hold this is impossible because $a_0=0$ would imply that the coeff of $x$ is zero
