TITLE: Distance traveled by a bouncing ball with exponentially diminishing rebounds
QUESTION [5 upvotes]: This is kind of an odd question, but can somebody please tell me that I am crazy with the following question, I did the math, and what I am told to prove is simply wrong:
Question:
Show that a ball dropped from height of h feet and bounces in such a way that each bounce is $\frac34$ of the height of the bounce before travels a total distance of 7 h feet.
My Work:
$$\sum_{n=0}^{\infty} h \left(\frac34\right)^n = 4h$$
Obviously 4 h does not equal 7 h .  What does the community get?
I know that my calculations are correct, see Wolfram Alpha and it confirms my calculations, that only leaves my formula, or the teacher being incorrect...
Edit:
Thanks everyone for pointing out my flaw, it should be something like:
$$\sum_{n=0}^{\infty} -h + 2h \left(\frac34\right)^n = 7h$$
Thanks in advance for any help!

REPLY [5 votes]: To get symmetry - a complete sawtooth pattern - suppose the ball is first thrown up from ground to height $h$. The total distance $x$ is that of the first tooth $= 2h$ plus the remaining sawtooth $= 3/4\ x$. Thus $x =\: 2h + 3/4\ x,\ $ so $x = 8h\:.\ $ Subtracting the intitial throw up leaves $7h.$