Basic Probability Question

I came across a approximation for another expression in an intro to probability book, but I couldn't see why it holds. The probability of not getting multiples in a sample space "r" of a population "n" is given (n)!/(n-r)!(n^r). And the approximation when r is relatively small is "1-((1+2+...(r-1))/n)" which of course is just 1-((r)(r-1)/2n). When r is quite a bit smaller than n I can see that the denominator doesn't "beat" the numerator quick, but I don't really see much more than that. Thanks.

Any response is appreciated as this may not be quite clear enough. Thanks again!