Combinations/ ancestor word problem

Question

A.) If you go back 10 generations, how many ancestors Do you have? count your parents as the first generation back, your four grandparents as the second generation back, and so on. (Assume there's no duplications)

 

B.) How many generations must you go in order to have more than one million ancestors? 

Answer 1

A)

2 parents (2¹)

4 grand parents (2²)

8 great grand parents (2³)

....

2¹⁰

 

B) 

S_n = a₁(1 - rⁿ) / (1 - r))

1000000 = 2(1 - 2ⁿ) / (1 - 2)

500000 = (1 - 2ⁿ) / (-1)

500000 = 2ⁿ - 1

500001 = 2ⁿ

ln 500001 = n ln 2

13.1223654 ≈ 0.693147181 n

18.931 ≈ n

 

You have more than one million ancestors after 19 generations.