/sci/ - Science & Math

For part a, is this answer correct?
The ball drops from initial height H, so + H to start, then it bounces up and down for 2Hr^n. So to find the distance it travels (the sum of the initial drop and subsequent bounces), let S_n denote the series without the intial drop factored in, so that the total is S_n + H. Let D denote the total distance traveled, S_n + H.
[eqn]

S_n = 2Hr + 2Hr^{r+1} + .. + 2Hr^n = 2(Hr + Hr^{r+1} + .. + Hr^n)\\
rS_n = 2(Hr + Hr + Hr^{r+1} + .. + 2r^{n+1}) \\
S_n - rS_n = 2(Hr - Hr^n)\\
S_n = 2\frac{Hr(1-r^{n-1}}{1-r})\\
D = H + \sum_{n = 1}^{\infty} = H + \frac{2Hr(1 - r^{n-1})}{r-1}
[/eqn]

If this is correct, how do begin part b?
>>11561677
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