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Homework Help: Spivak Calculus- Chapter 1, Q1(v)

  1. Oct 13, 2009 #1
    1. The problem statement, all variables and given/known data

    Prove the following:
    xn-yn= (x-y)(xn-1+xn-2y+ … + xyn-2+yn-1)

    3. The attempt at a solution

    What do the 3 full stops (...) mean?
    I didnt know where to start, so I tried to subsitute a number for n, I said n=5, I then multiplied out the brackets and removed terms that were cancelled out through opposite signs. This leaves me with:

    = x5+x2y3-x3y2-y5

    and from there I am stuck.

    extra - ANY ADVICE?

    I am from the UK, I have finished my undergraduate degree in Ocean Science where we used equations but did not have to derive them and am looking to take a masters in physical oceanography. I have not studied maths since GCSE, and to do the masters I need to know calculus and physics. I looked into taking courses but could not find any suitable for me to do within a few months.

    I have University Calculus (Hass,Weir & Thomas) and University Physics (Young and Freedman) which were bought for me by my professor who has encouraged me to improve my maths and physics because he thinks I am capable of doing well in physical oceanography. In addition I have bought Spivaks Calculus book after reading the reviews online and have just started with the 1st chapter.

    Does anyone have any advice for me as I am starting out?
  2. jcsd
  3. Oct 13, 2009 #2


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    Homework Helper

    the "..." just means there are other terms, if you notice it is following a pattern.

    You could just expand it....

    (x-y)(xn-1+xn-2y+xn-3y+ … + xyn-2+yn-1) = x( (x-y)(xn-1+xn-2y+xn-3y+ … + xyn-2+yn-1))-y( (x-y)(xn-1+xn-2y+xn-3y+ … + xyn-2+yn-1))

    you should notice some things cancel out.
  4. Oct 15, 2009 #3
    Excellent, thank you!
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