up blocked

hi i want tell me what to do to prove the following it is up blocked 

αν=ν!/ν^ν i think with berrnulli,(general say:(1+x)^ν ≥ 1+χν 

so in this case :       

v!=1 x 2 x...x (v-1) x v  and v^v with bernulli : v^v=(1+(v-1))^v ≥ 1+(v-1)v   (x is the symbol of multiplication) 

                        1 x 2 x...x (v-1) x v        1 x 2 x...x (v-1) x v 

so :       αν ≤     -------------------------  ≤  --------------------------- =   1 x 2 x...       but i want it be = 1 

                               1+(v-1)v                        (ν-1)ν                     

Please i want your help.Sry for my bad english