Anyone answer this calculation.

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In summary, the conversation was about a question regarding the sum of money given over 30 days when starting with $1 and doubling it each day. The solution involves a geometric sum formula and results in a total of $1073741823.
  • #1
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I have been asked this question before 6 months, it was an interesting question.

Here is the question i just want to share.
Today let me simplify it as 1st day i give 1 $ 2nd Day i double it to 2$ I am going to give you like this for 30 days how much money i would have totally given at the end of 30 days... this is the question initially i thought simple and i found there is really a calculation behind it. I leave it to the members to find out the answer.
 
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  • #2
Sum((n-1)^2,n=1,30)

Don't know what the number is.
 
  • #3
No, "doubling" would be [itex]2^{n-1}[/itex], not [itex](n-1)^2[/itex].

And the sum: [itex]\sum_{n=1}^{30} 2^{n-1}[/itex] is a geometric sum. A geometric sum is of the form [itex]\sum_{n=0}^N ar^{n-1}[/itex]. It is well known that it totals
[tex]a\frac{1- r^{N}}{1- r}[/tex]
For a= 1, r= 2, that is
[tex]\sum_{n=0}^N= \frac{1- 2^N}{1- 2}= 2^{N}- 1[/tex]
For n= 30, that is 230-1= 1073741823.
 
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  • #4
THanks Halls of Ivory. I switched the base and exponent.
 
  • #5
Couldn't you just do

[tex]30!=2.6525286\cdot10^{32}[/tex]

Edit: Never mind, I read the original question wrong.
 
  • #6
Ok david you have worked it out well, what is the answer in $
 

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