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## Homework Statement

Use the binomial expansion (1± x)

^{n}= 1± nx + (n(n-1)/2) x

^{2}±....

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/r

^{2}

## 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

_{E}

^{n}(1±Δr/r

_{E})

^{n}

I plugged this into the equation for gravitational acceleration and got

g=GM/[r

_{E}

^{n}(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 :)