Can you help me calculate the following limit ?
$\lim_ {n \to \infty} \frac{ 1- (1-\frac{1}{n} )^4 }{1- (1-\frac{1}{n})^3 }$
Intuitively, I can see that the numerator decays to zero much faster than the denominator. But how can I show it formally? (I tried to divide by $ \frac{1}{n} )^4 $ and by $\frac{1}{n})^3$ but without any success.
Help?
Thanks!