KöMaL 2010 B4310

Let $a_0,a_1,\ldots,a_n$ be positive numbers, such that $a_{k+1}$-$a_k \ge$1 for all $k$=0,1,...,$n$-1. Show that $1 + \frac1{a_0} \left(1+\frac1{a_1-a_0}\right) \cdots \left(1+\frac1{a_n-a_0}\right) \le \left(1+\frac1{a_0}\right) \left(1+\frac1{a_1}\right) \cdots \left(1+\frac1{a_n}\right).$