Hi!

How do I show that

$\displaystyle \lim_{n\to\infty}\int_0^1 \frac{1}{\sqrt{1-x^n}} \, dx =1$ ?

I've proved that

$\displaystyle \int_0^1 \frac{1}{\sqrt{1-x^n}} \, dx=\frac{\sqrt{\pi}}{n} \frac{\Gamma(\frac{1}{n})}{\Gamma(\frac{1}{n}+\fra c{1}{2})} $

Thanks!