BINOMNI KOEFICIJENTI
BINOMNI KOEFICIJENTI
BINOMNI KOEFICIJENTI
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<strong>BINOMNI</strong> <strong>KOEFICIJENTI</strong><br />
Teorem 6<br />
( )( ) ( )( ) ( )( )<br />
n r n n − k n n − r + k<br />
= =<br />
.<br />
r k k r − k r − k k<br />
Dokaz: ( )( )<br />
n r<br />
=<br />
r k<br />
=<br />
n!<br />
k!(n − k)! ·<br />
n!<br />
r!(n − r)! ·<br />
Druga jednakost dokazuje se analogno!<br />
r!<br />
k!(r − k)! = n!<br />
(n − r)!(r − k)!k! =<br />
( )( )<br />
(n − k)!<br />
(r − k)![n − k − (r − k)]! = n n − k<br />
.<br />
k r − k<br />
() 21. studenog 2011. 13 / 27