Spivak Calculus- Chapter 1, Q1(v)

[MathsLearner]

Homework Statement

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

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 canceled 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!

 

[rock.freak667]

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

You could just expand it...

(x-y)(x^n-1+x^n-2y+x^n-3y+ … + xy^n-2+y^n-1) = x( (x-y)(x^n-1+x^n-2y+x^n-3y+ … + xy^n-2+y^n-1))-y( (x-y)(x^n-1+x^n-2y+x^n-3y+ … + xy^n-2+y^n-1))


you should notice some things cancel out.

 

[MathsLearner]

Excellent, thank you!