Chapter 12 Sequences and Series - 12.4 Find Sums of Infinite Geometric Series - 12.4 Exercises - Problem Solving - Page 825: 41d

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The total distance traveled by the ball is $h+2\sum^{\infty}_{r=0}(h\times 0.75)(0.75)^{i-1}+8\\=h+2\sum^{\infty}_{r=0} 0.75h(0.75)^{i-1}\\=h+\frac{2a_1}{1-r}\\=h+\frac{2(0.75h)}{1-0.75}\\=h+\frac{2(0.75h)}{0.25}\\=7h$