SOLUTION: What is 1 penny doubled 64 times?

Question 1055358: What is 1 penny doubled 64 times?
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
184,467,440,737,095,516.15
:
no. pennies given on second day 2
------------------------------- = --- = 2
no. pennies given on first day 1
:
no. pennies given on third day 4
------------------------------- = --- = 2
no. pennies given on second day 2
:
no. pennies given on fourth day 8
------------------------------- = --- = 2
no. pennies given on third day 4
:
As you see, the ratio of the geometric series that gives the total number of pennies any time we double the last total is 2. We can now use the fact that the sum of a geometric series (called S) with n terms whose ratio is r is the following:
:
S = (first term)(1-r^n)/(1-r)
and we have a first term 1 and a ratio of 2, let's find the sum after 64 times:
1(1-2^n)/(1-2) = -(1-2^n) = 2^n-1
= 2^64-1 = use your calculator, you'll get: 184,467,440,737,095,516.15
(184 quadrillion, 467 trillion, 440 billion, 737 million, 095 thousand, 516 hundred and 15 cts.)

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