The change in potential energy when a body of mass m is raised to a height n R from the surface of the earth ( R = radius of the earth)

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The change in potential energy in gravitational field is given by $∆ E = G M m (\frac{1}{r_{1}} - \frac{1}{r_{2}})$

In this problem; $r_{1} = R$ and $r_{2} = n R$

$∆ E = G M m (\frac{1}{R} - \frac{1}{n R})$

$= \frac{G M m}{R} (\frac{n - 1}{n})$

$= m g R (\frac{n - 1}{n}) (∵ g = \frac{G m}{R^{2}})$

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