A space ship, at rest in a certain reference frame S, is given a speed increment of 0.46c (call this boost 1). Relative to its new rest frame, the spaceship is given a further 0.46c increment 12s later (as measured in its new rest frame; call this boost 2). This process is continued indefinitely, at 12s intervals, as measured in the rest frame of the spaceship. Assume that each boost takes a negligibly short time compared with 12s.

1. derive an equation that gives the velocity of the ship after any boost n (n==1,2,3,4....)

2. show the value of the "gamma function for boosts 1,.2,3,...10 gamma = [1-(v^2/c^2)]^.5......c= speed of light in meters/sec