A rover operating on Mars measures changes in gravitational pull as it climbs a steep hill of height ∆z, where ∆z is much smaller than R_Mars (the radius of Mars). Use the binomial expansion

(1 ± x)ⁿ = 1 ± nx + (n(n-1)/2) x² ± ...

to derive the formula approximating the change in acceleration due to gravity in Mars $\Delta g_{\text{Mars }}$, where $g_{Mars}$ is the gravitational acceleration at Mars's surface.