Posted by **fred** on Sunday, July 18, 2010 at 3:53pm.

A ball has bounce coefficient 0 < r < 1 if when it is dropped from height h, it bounces back to a height of rh. Suppose that such a ball is dropped from an initial height a and subsequently bounces infinitely may times. Find the total up-and-down distance in all its bouncing.

- calculus -
**drwls**, Sunday, July 18, 2010 at 4:17pm
h[1 + 2r + 2r^2 + 2r^3 + ...]

= 2h(1 +r +r^2 + r^3 + ..) -h

= 2h [1/(1-r)] -h

- calculus -
**bobpursley**, Sunday, July 18, 2010 at 4:19pm
distance= h+2hr+2hr^2+2hr^3...

distance= 2h+2hr+ 2hr^2+... -h

Isn't that an geometric series?

http://en.wikipedia.org/wiki/Geometric_progression

sum= a/(1-r) -h= 2h/(1-r) -h

check my thinking

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