BINOMNI KOEFICIJENTI
BINOMNI KOEFICIJENTI
BINOMNI KOEFICIJENTI
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<strong>BINOMNI</strong> TEOREM<br />
Drugi tip identiteta dobivamo tako da u binomnom teoremu uvrstimo razne zgodno<br />
odabrane kompleksne brojeve.<br />
Teorem 10<br />
Neka su n,q ∈ N, 1 ≤ q ≤ n − 1, r ∈ {0, 1, . . . , q − 1}. Tada je<br />
( ) ( ) ( )<br />
n n n<br />
+ + + . . . = 1 q−1<br />
∑<br />
r r + q r + 2q q<br />
k=0<br />
(<br />
2cos kπ ) n<br />
cos<br />
q<br />
k(n − 2r)π<br />
.<br />
q<br />
Teorem 11 (Binomni red)<br />
Za z ∈ C, |z| ≤ 1 i sve α ∈ R vrijedi<br />
(1 + z α ) =<br />
( )<br />
∞∑ α<br />
z α .<br />
k<br />
k=0<br />
() 21. studenog 2011. 23 / 27
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