Binomialrekken
Binomialrekken
Binomialrekken
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<strong>Binomialrekken</strong> – Eksempel<br />
Har<br />
( )<br />
1<br />
∞∑<br />
1 + x = (1 − −1<br />
x)−1 = x n , |x| < 1<br />
n<br />
n=0<br />
( ) ( ) ( )<br />
−1 −1 −1<br />
= + x + x 2 + · · ·<br />
0 1 2<br />
( )<br />
−1<br />
=<br />
n<br />
( )<br />
−1<br />
= 1,<br />
0<br />
( )<br />
−1<br />
= −1<br />
1<br />
(−1)(−1 − 1)(−1 − 2) · · · (−1 − n + 1)<br />
n!<br />
= (−1) n n!<br />
n! = (−1)n
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