Multiple collisions

A block of mass mm sits on a horizontal, frictionless surface some distance \ell from a wall. Another block of mass MM collides from the right with velocity V.V. Depending on that ratio x=Mm,x =\frac Mm, the blocks will collide a total of nn times.

Find limxnx.\displaystyle \lim_{x\rightarrow \infty} \frac{n}{\sqrt{x}}.

Assume that all collisions are elastic and that the motion is in 1-dimension.

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