MHB Taylor Series Expansion and Radius of Convergence for $f(x)=x^4-3x^2+1$

[ineedhelpnow]

find the taylor series for $f(x)=x^4-3x^2+1$ centered at $a=1$. assume that f has a power series expansion. also find the associated radius of convergence.

i found the taylor series. its $-1-2(x-1)+3(x-1)^2+4(x-1)3+(x-1)^4$ but how do i find the radius of convergence?

 

[Euge]

Since your Taylor series is a polynomial in $x$ (or $x-1$), it converges for all $x$. So the radius of convergence is $(-\infty, \infty)$.