Gravitation and Binomial Expansion

[novicephysicist]

Homework Statement

Use the binomial expansion (1± x)ⁿ = 1± nx + (n(n-1)/2) x² ±...
to show that the value of g is altered by approximately Δg ≈ -2g(Δr/r_E) at a height Δr above the Earth's surface, where r_E is the radius of the Earth, as long as Δr<<r_E

Homework Equations

g=GM/r²

The Attempt at a Solution

I had completely forgotten binomial expansions, so I looked it up and found an equation that seemed to apply:
x=Δr/r_E
and then
(Δr±r_E) = r_Eⁿ(1±Δr/r_E)ⁿ
I plugged this into the equation for gravitational acceleration and got
g=GM/[r_Eⁿ(1±Δr/r_E)ⁿ]²
I'm not sure if I should substitute 2 for the n? Honestly I'm not sure where to go from here at all. Hopefully I did something correctly? (Note: this is my first time on Physics Forums, so I hope I formatted this correctly and everything)

Any help would be appreciated, thank you :)

 

[novicephysicist]

Never mind, I figured it out!