The equipment in our laboratory consists of an infinitely long inclined plane at 45 degrees to the vertical and a ball, which bounces with no loss in energy.

The ball is dropped from some height above the plane, bounces on its way down the plane (Boing! Boing!).

The laboratory investigator records:

T(N) = the time between the Nth and (N+1)th bounce, and

H(N) = the maximum distance between the ball and the plane between the Nth and (N+1)th bounce.

Write an expression for

H(N+1)T(N+1)/( H(N)T(N) ) as a function of N.