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a ball is dropped from a height of 40cm onto a horizontal surface and bounces in a vertical line until it eventually stops on the surface.
the ball bounces in such a way that it loses ten percent of its height for each bounce and will continue to do this until it comes to rest on the surface.

what is the total distance travelled by the ball before coming to rest on the surface?how do i calculate this?

The sequence of successive heights can be written as
h---40 + 40(.9) + 40(.9^2) + 40(.9^3) +........ or
40(1 + .9 + .9^2 + .9^3 + ......

The limit of the converging series Sn = 1 + r + r^2 + r^3 + r^4 + = 1/(1 - r) -1 < r < 1

Thus, the total distance traveled becomes D = 40(1)/(1 - .9) = 40/.1 = 400 cm.

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