A person has 2 parents, 4 grandparents, 8 great-grandparents, and so on. Find the number of his ancestors during the ten generations preceding his own.
Answer: B
The number of ancestors forms a G.P.: 2, 4, 8, ... up to 10 terms. Here, \(a=2, r=2, n=10\). The sum is \(S_n = a\frac{r^n-1}{r-1}\). \(S_{10} = 2\frac{2^{10}-1}{2-1} = 2(1024-1) = 2(1023) = 2046\).