Re: HSC 2013 4U Marathon
Here's my go at the question. I'll just do the left inequality and presume the right inequality is similar.
\frac{x^{n+1}-y^{n+1}}{x-y}=x^n+x^{n+1}y+...+xy^{n-1}+y^n
=y^n(1+\frac{x}{y}+\frac{x^2}{y^2}+...+\frac{x^n}{y^n})>y^n(n+1)
As \left ( \frac{x}{y} \right )^k>1
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