Answer
65,534
Work Step by Step
The nth partial sum of a geometric sequence
$S_{n}=\displaystyle \sum_{k=1}^{n}ar^{k-1}$ (where $r\neq 1$)
is given by$ \displaystyle \quad S_{n}=a\cdot\frac{1-r^{n}}{1-r}$
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The sequence (of ancestors per generation)
2, 4, 8, 16, ... $2^{n}$...
is a geometric sequence with $a=2$ and $r=2$.
The total number of ancestors in n=15 generations:
$S_{15}=2\displaystyle \cdot\frac{1-2^{15}}{1-2}=2(2^{15}-1)=65,534$,
