Question 65739: Please help me figure out this word problem. Considering yourself, your parents, your grandparents, and so on, back to your grandparents with the workd "great" used in front 40 times. What is the total number of people that you are considering. Thanks for your help.
Found 2 solutions by ntnk, stanbon:
Answer by ntnk(54)   (Show Source):
You can put this solution on YOUR website! Each level is 2^x (because each person has two parents and so forth.)
Therefore,
YOU are 2^0 = 1 (person);
PARENTS are 2^1= 2 (people);
GRANDPARENTS are 2^2= 4 (people);
GREAT GRANDPARENTS are 2^3=8;
GREAT GREAT GRANDPARENTS are 2^4=16;
GREAT GREAT GREAT GRANDPARENTS are 2^5=32;
and so forth.
But notice that three "greats" implies 2^5.
This means that x "greats" implies x+2. Therefore, 40 "greats" implies 2^42, which is the total number of people that you are considering.
Also, the question is a bit unclear as to if you want to know the total number of people including yourself and parents, and grandparents, and so forth until great*40 grandparents, so if you include ALL of those people, then it will be 2^42+2^41+2^40+...+2^20+2^19+...+2^3+2^2+2^1+2^0 and so forth.
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Parents=2
Grand parents=4=2^2
"Great" starts with 2^3 people
Each generation before that multiplies by 2
The last generation you want has 2^3*2^39=2^42
which is a very large number.
Comment: I can't tell if you are starting the count with yourself:
if you are the total number is:
1+2+2^2+2^3+...+2^42
Using the sum formula with r=2 and n=41 the sum is:
S(41)=1[2^(42)-1]/[2-1]
=2^42-1
=4.398046511x10^12
Cheers,
stan H.
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