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I need help on this,basic stuff

  1. Mar 18, 2007 #1
    let * be either + or - ( you can use both of them)

    then let 1*2*3*4*..............*2004*2005*2006

    The question is this, what would be the smallest natural number that you would get, after you do the neccessary calculations?

    i got the answer 1.
    here is what i did:

    (2006-2005)-(2004-2003)-...........-(4-3)+(2-1)=1

    so can anyone please comment on my approach?

    thnx
     
  2. jcsd
  3. Mar 18, 2007 #2

    matt grime

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    Such as what? 1 is the smallest natural number for most people (for some it is 0). Though I don't think you have the minus signs quite right. What you've written appears to go, after simplifying brackets

    1-1-...-1+1, which is really about -998. But you have a good idea.
     
    Last edited: Mar 18, 2007
  4. Mar 18, 2007 #3
    what if i go like this then:
    (2006-2005)-(2004-2003)+(2002-2001)-(2000-1999)+...............+(6-5)-(4-3)+(2-1)=1

    But how would know whether 1 or zero or any other result is the right answer

    1-1+1-1+1-1+1-1+......+1-1+1=1
     
    Last edited: Mar 18, 2007
  5. Mar 18, 2007 #4

    matt grime

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    You're asked to find the smallest natural number. Since you can find 1, and that is commonly taken to be the smallest natural number, then what is it you want to ask?
     
  6. Mar 18, 2007 #5
    i want to know that, how can i be sure that my way of solving the problem is correct, and ishould not approach the problem differently instead?
    thnx
     
  7. Mar 18, 2007 #6

    matt grime

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    But you've found, by a perfectly valid method, that you can get 1, and since 1 is (for the purposes of this question) the smallest natural number, we are done. There really isn't anything to worry about. There is no such thing as *the* way to solve a question that you must use (unless instructed to do so explicitly in the question e.g. "prove by induction that..."). But there are no constraints here.
     
  8. Mar 19, 2007 #7
    thank you indeed
     
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