I have stuck in the middle of a problem and I don't know whether or not the following inequality is true.
$$\sum_{i=0}^{[n\,t]} \Bigl(1-\frac{i}{n\,t}\Bigr)^{n-1}>t$$
Assuming that $n$ is a natural number and $t$ is a positive real number and $[x]$ is the floor function.