Limit of a sequence : How do I compute the following limit 
$$ \lim_{ n\rightarrow \infty  }{ { \left  (\frac { \sqrt [ n ]{ a } +\sqrt [ n ]{ b } +\sqrt [ n ]{ c } +\sqrt [ n ]{ d }  }{ 4 } \right ) }^{ n } }  $$
$a,b,c,d\geq0$ 
Thanks.

Using the elementary limits $\lim_{n\to\infty} (1+1/n)^n=e$ and $\lim_{x\to 0} (a^x-1)/x=\ln a, \space a>0$, we get
$$\lim_{ n\rightarrow \infty  }{ e^{ \left  (\displaystyle n \frac { \sqrt [ n ]{ a } +\sqrt [ n ]{ b } +\sqrt [ n ]{ c } +\sqrt [ n ]{ d }-4  }{ 4 } \right ) } }={ e^{\displaystyle \frac{1}{4}\lim_{ n\rightarrow \infty  } \sum_{abcd} (t^{1/n}-1)/(1/n)}}=(abcd)^{\frac{1}{4}}.$$
Q.E.D.
