BINOMNI KOEFICIJENTI
BINOMNI KOEFICIJENTI
BINOMNI KOEFICIJENTI
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<strong>BINOMNI</strong> <strong>KOEFICIJENTI</strong><br />
- definirali smo ih za sve nenegativne brojeve n i r.<br />
( )<br />
n<br />
Za r > n vrijedi = 0.<br />
r<br />
( )<br />
n<br />
Za svaki n ∈ N imamo = 1.<br />
0<br />
( )<br />
n n! n(n − 1) · · · (n − r + 1)<br />
Za n ∈ N i 1 ≤ r ≤ n imamo = = .<br />
r r!(n − r)! r!<br />
Teorem 1<br />
( ) ( )<br />
n n<br />
= ,<br />
r n − r<br />
( ) ( ) ( ) ( )<br />
n<br />
= n n − 1 n n − 1<br />
⇒ r = n .<br />
r r r − 1 r r − 1<br />
() 21. studenog 2011. 2 / 27