{"conversations": [{"from": "user", "value": "Podries simplificar la seg\u00fcent expressi\u00f3 matem\u00e0tica? C( N-1, n-1) / C( N, n)"}, {"from": "assistant", "value": "Entenc que la notaci\u00f3 C ( N, n ) es refereix al nombre combinatori de N sobre n. En aquest cas la simplificaci\u00f3 \u00e9s senzilla, aix\u00ed que pas a detallar- la: C ( N + 1,n + 1 ) / C ( N,n ) = (. (N + 1 )! / ( n + 1 )! \u00b7 ( N + 1- ( n + 1 ) )! ) / (N! \u00b7 ( n! \u00b7 N + 1 ) ) ( N + 1 )! \u00b7 n! \u00b7 n + 1 )! / ( n + 1 )! / ( n + 1 )! / ( n + 1 ) ( N + 1 ) ( N + 1 ) )! \u00b7 l (N + 1 ) ( n + 1 ) ( n + 1 ) per\u00f2, per la pr\u00f2pia! l'estatu! 1) recursiva de factorial tenim que (N + 1 ) ( N + 1 ) =) \u00b7 N + 1 ) i que (nd + ct) \u00b7 c = ct ( N = ct ) ( N + 1 ) ( n ) en el punt) \u00b7 t ) ( st )"}]}