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

1. Oct 13, 2009

### MathsLearner

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?
Thanks!

2. Oct 13, 2009

### rock.freak667

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.

3. Oct 15, 2009

### MathsLearner

Excellent, thank you!

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