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!