Very very very annoying maths question - PLEASE HELP!!!!!!!!!!!!!

Discussion in 'Off-Topic Chat' started by groovy, Mar 17, 2005.

  1. groovy

    groovy Active Member

    Argh I'm stuck on this question, and the worst part is I'm sure the answer is very obviously staring me in the face.

    "A sequence of numbers can be grouped and added together as shown.

    The sum of 2 numbers: (1 + 2) = 4 - 1
    The sum of 3 numbers: (1 + 2 + 4) = 8 - 1
    The sum of 4 numbers: (1 + 2 + 4 + 8 ) = 16 - 1
    The sum of 5 numbers: (1 + 2 + 4 + 8 + 16) = 32 - 1 etc

    Find a formula for the sum of the first n numbers of this sequence."

    Please help!
     
    Last edited by a moderator: Mar 17, 2005
  2. BigHorn

    BigHorn Active Member

    . n
    .2 - 1


    sorry difficult to write two to the power n minus 1
     
  3. groovy

    groovy Active Member

    ?

    Do you mean (n/2) - 1


    EDIT: oh so you mean 2to the power n, -1?
    hamng on while I try and sort my brain.....
     
  4. groovy

    groovy Active Member

    Yes you've got it!!!!!! thank you sooo much!!! I was so nearly there but my brain was tying in knots!
     
  5. lilcornetgirl

    lilcornetgirl Member

    Im not sure if this is correct as im only ickle and i dunno maths that good but i think its n to the power of 2 - 1 so if your writing it down itd be

    n2-1

    apart from the 2 would be small at the top of the n. I hope this is right and i dont look a total fool.
     
  6. Jan H

    Jan H Moderator Staff Member

    no, I think bighorn was right. it's (2 to the power n)-1 (in most mathematical programming languages, it would be written as 2^n - 1)
     
  7. TheMusicMan

    TheMusicMan tMP Founder Staff Member

    Here you go, how's this...

    [​IMG]
     
  8. Jan H

    Jan H Moderator Staff Member

    No, sorry.

    Actually, I now think the solution should be 2^(n+1) - 1

    n=1 -> 2^2 - 1 = 4-1 = 3
    n=2 -> 2^3 - 1 = 8-1 = 7
    n=3 -> 2^4 - 1 = 16-1 = 15
    n=4 -> 2^5 - 1 = 32-1 = 31
    etc.

    it all depends on what you consider to be the first number of the sequence (n=1) of course...
     
  9. Big Twigge

    Big Twigge Active Member

    I love algebra!
     
  10. lynchie

    lynchie Active Member

    it's like sandwich making... but with numbers...
     
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  12. TheMusicMan

    TheMusicMan tMP Founder Staff Member

    [​IMG]
    Is this better?
     
  13. Jan H

    Jan H Moderator Staff Member

    :tup


    :tongue:
     
  14. TheMusicMan

    TheMusicMan tMP Founder Staff Member

    Cheers Jan...

    just in case anyone is wondering how this is done... it is obviously a screen capture as I don't have a LaTeX system installed on the tMP server to display algebra or equations. I did the originals using the Equation Editor in MS Word... easy eh!

    Insert > Object > Create New Tab > Microsoft Equation 3.0
     
  15. Jamie

    Jamie Member

    Not tried to get my head round this sort of stuff for a while, but they were right in the first place. I make it, in words, 2 to the power of n, minus 1.


    n= 1, 2, 3, 4, 5, 6

    sum (term)= 1, 3, 7, 15, 31, 63

    gap between consecutive terms= 2, 4, 8, 16, 32


    (really hard to show this here... imagine those numbers are arranged so that you can read down the columns!)


    If you look at the pattern of the numbers of the gaps between terms (2, 4, 8, 16...), they're powers of two, thus 2^n has to be in the formula somewhere.

    So, if you take n to be anything, and perform this function on it, you'll see what else needs doing to it in order to get to the sum you're after. (really not explaining self well!!)

    For example, for n=3. 2^n= 2^3= 2*2*2= 8. We need 7, so -1. Thus 2^n-1.

    To check, for n=5. 2^n= 2^5= 2*2*2*2*2= 32. We need 31, so-1, Which confirms, 2^n-1

    Am I doing this right?!
     
  16. neiltwist

    neiltwist Active Member

    looks good to me.
     
  17. yonhee

    yonhee Active Member

    *looks confused*
    Is this clever people maths?
     
    Last edited: Mar 19, 2005
  18. lynchie

    lynchie Active Member

    ah no, clever people maths is much more long winded and annoying... as I'm beginning to realise...
     
  19. yonhee

    yonhee Active Member

    so what maths is it?
    Why are you doing clever people maths?
     
  20. MoominDave

    MoominDave Well-Known Member

    Oh crikey, you're not doing Maths while you're at Warwick, are you? Sounds like they still haven't learnt how to make it appealing! Don't worry, there is a salvation beyond it, but it involves becoming a Physicist...
     
  21. bandcampgal

    bandcampgal Member

    (2^n)-1 is rite i think

    (im doin maths degree so i technically shud no, but that aint necessarily the case!)
     
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