The magnitude of the gravitational force exerted by the Earth on an object of mass m at the Earth's surface is
Fg = G*M*m/ R^2
where M and R are the mass and radius of the Earth.
Let's say the object is instead a height y << R above the surface of the Earth. Using a Taylor series or binomial expansion, find a polynomial expression in y for the force of gravity acting on this object, correct to first order (i.e., in this case, the lowest "non-trivial" order of the Taylor series).
taylor series equation
The Attempt at a Solution
I set up the equation as Fg=G*M*m/(R+y)^2 centered around y=0
I'm just lost on how to set this up, what is the right equation and point to center around?