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Anyone answer this calculation.

  1. Dec 25, 2009 #1
    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$ im 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.
  2. jcsd
  3. Dec 25, 2009 #2

    Don't know what the number is.
  4. Dec 25, 2009 #3


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    Science Advisor

    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.
    Last edited by a moderator: Dec 26, 2009
  5. Dec 25, 2009 #4
    THanks Halls of Ivory. I switched the base and exponent.
  6. Dec 25, 2009 #5
    Couldn't you just do


    Edit: Never mind, I read the original question wrong.
  7. Dec 27, 2009 #6
    Ok david you have worked it out well, what is the answer in $
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