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1

Tennis ball touch down 10 times, and bounce 9 times.

Down ↓ 16, 8, 4, 2, ...

Up ↑ 8, 4, 2, ...

So, we have two geometric sequences, were each number, after the first is twice less than previous. The only difference between them is
16.
Let's find the sum of the numbers of second geometric sequence ( Up ) ~~~~~~~~~~~~~~~~~ 1 - r^{n} S_{9} = a_{1} • ————
1 - r

a_{1} is the first term of geometric sequence,
r is the common ratio n is the number of terms ~~~~~~~~~~~~~~~~~~~~
a_{1} = 8
r = 1/2
n = 9
1 - (1/2)^{9}
S_{9} = 8 · —————— =
1 - (1/2)

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