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## Homework Statement

A body falls vertically from rest. During the nth second it falls a distance d. Prove that by the end of the nth second it has fallen a total distance (D) of (2d+g)^2/8g

## Homework Equations

x = x0 + V0 + 1/2at^2

where

x0 = initial position

v0 = initial velocity

a = acceleration

t = time

## The Attempt at a Solution

The total distance is D = 1/2gn^2 because the object has fallen for n seconds. At the end of the first second d=D and t^2 = 2d/g. I'm unsure about how to proceed from here. Any help gratefully received...