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Prove that

$f\left( x\right) =\dfrac {1-x^{n}} {\left( 2-x\right) ^{n}-1}, \quad x\in [0,1)$

is convex for any $n\in \mathbb{N}$.

The second derivative is very unfriendly for a calculus...

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    Can somebody show that x-\frac{1-x^n}{(2-x)^n-1}+\frac{1}{2^n-1}>0? I think this proves it.2012-08-19

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