(A+B)^n=A^n+nA^(n-1)B+(n(n-1)/2!)A^(n-2)B^2+(n(n-1)(n-2)/3!)A^(n-3)B^3+...
Let A=2, B=-x, and n=-5, then (2-x)^-5=2^(-5)+5(2^-6)x+15(2^-7)x^2+35(2^-8)x^3=
1/32+5x/64+15x^2/128+35x^3/256.
Let A=3, B=-x, and n=½, then (3-x)^½=3^½-(3^-½)x/2-(3^-3/2)x^2/8-(3^-5/2)x^3/16.
3^-½=1/√3=√3/3; 3^-3/2=1/3^3/2=1/3√3=√3/9; 3^-5/2=1/9√3=√3/27.
Expansion becomes: √3-x√3/6-x^2√3/72-x^3√3/432.
This reduces to √3(1-x/6-x^2/72-x^3/432).
Let A=1, B=-2x, n=-½, then √(1/(1-2x))=1+x+3x^2/2+5x^3/2.