You have two parents, four grandparents, eight great-grandparents, and so forth. (a) If all your ancestors were distinct, what would be the total number of your ancestors for the past 39 generations (counting your parents' generation as number one)

From the first generation = 2 ancestors.

From the second generation = 4 ancestors or (2)^2 ancestors.

From the third generation = 8 ancestors or (2)^3 ancestors.

We can infer from the given data, each consecutive generation possesses twice the number of members.

The sum will be:

2 + 4 + 8 + 16 + ... + (2)^39

To evaluate the amount of ancestors, let's employ the formula for the summation of a geometric sequence.

(Geometric sequence shows the sequence of numbers that varies by a specific factor. This factor is specifically known as a ratio).

Formula for Geometric sequence:

S = (a1) × 1 - (r)^n

1 - r

Take:

S -> sum

a1 -> first member of a sequence

r -> ratio

n -> number of elements

In this question, our:

a1 = 2; r = 2; and n = 39

S = (2) × 1 - (2)^39

1 - 2

S = 1,099,511,627,777

i think it is the third one.