let rec liste_privee_dernier_elt l = match l with
              [] -> failwith "liste vide"
             |[a] -> []
             |t::r -> t:: liste_privee_dernier_elt r;;

let tete_liste l = match l with
              [] -> failwith "liste vide"
             |[a] -> a
             |t::r -> t;;

let reste_liste l = match l with
              [] -> failwith "liste vide"
             |[a] -> []
             |t::r -> r;;

let est_singleton l = match l with
              [a] -> true
             |_ -> false;;

let rec liste_privee_dernier_elt_sf l =
 if l=[] then
  failwith "erreur: liste vide"
 else
  if (est_singleton l) then
   []
  else tete_liste(l)::(liste_privee_dernier_elt_sf (reste_liste l));;


let rec suite u0 a b n = if n=0 then u0 else a *. (suite u0 a b (n-1)) +. b;;

let rec serie u0 a b n = if n=0 then u0 else (suite u0 a b n) +. serie u0 a b (n-1);;

let rec membre x l = match l with
            [] -> false
           |t::r -> if x=t then true else membre x r;;

let rec liste_elt_diff l = match l with
            [] -> true
           |t::r -> if membre t r then false else liste_elt_diff r;;