Question 73431
This is a geometric progression.  Every term is double the preceding term.  Most beginning
math books will derive and show you the equation for the sum of the terms in a geometric
progression.
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This equation is:
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{{{S = (a(1-r^n))/(1-r)}}}
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where the variables are defined as:
S = the sum of the terms in the given progression
a = the first term.  In this problem the first term is 1
r = the common ratio.  In this problem the common ratio is 2 (terms are doubled) 
n = the number of terms.  In this problem n = 30
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Let's now just substitute numbers for this problem into the equation for the sum to get:
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{{{S = (1(1-2^30))/(1-2)}}}
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We can eliminate the multiplier 1 in the numerator, and the denominator becomes -1.
With these two changes the problem becomes:
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{{{S = (1-2^30)/(-1) = -(1-2^30) }}}
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A calculator will tell you that {{{2^30 = 1073741824}}}. Substituting this results in:
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{{{S = -(1-1073741824) = -(-1073741823) = 1073741823}}} dollars
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Not a bad deal. Start with a dollar on day 1 and 30 days later be worth $1,073,741,823.
A billionaire in just a month.
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Hope this helps you see how to work the problem.