BINOMNI KOEFICIJENTI
BINOMNI KOEFICIJENTI
BINOMNI KOEFICIJENTI
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<strong>BINOMNI</strong> <strong>KOEFICIJENTI</strong><br />
Teorem 2 Pascalova formula<br />
Za n,r ∈ N, 1 ≤ r ≤ n − 1 vrijedi<br />
( ) ( ) ( )<br />
n n − 1 n − 1<br />
= +<br />
r r − 1 r<br />
.<br />
Dokaz II:<br />
( ) ( )<br />
n − 1 n − 1 (n − 1)!<br />
+ =<br />
r − 1 r (r − 1)!(n − r)! + (n − 1)!<br />
r!(n − 1 − r)! =<br />
(<br />
(n − 1)! 1<br />
=<br />
(r − 1)!(n − 1 − r)! n − r + 1 )<br />
( )<br />
(n − 1)!<br />
=<br />
r (r − 1)!(n − 1 − r)! · n<br />
r(n − r) = n<br />
r<br />
() 21. studenog 2011. 4 / 27
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