The change in the gravitational potential energy when a body of a mass `m` is raised to a height `nR` above the surface of the earth is (here `R` is the radius of the earth)

Explanation

Change in `P.E. = P.E.` on the height `n R`
`- P.E.` on the surface of Earth
`= - (GMm)/((R + nR)) - (GMm)/(R )`
`= ((n)/(n + 1)) (GM m)/(R ) = ((n)/(n + 1)) mg R`