Page 165 - Fixtures

@ @pbjïØ Üa@ @QUP

nn ()

C (n,k)1n−k2k = C (n,k)2k
∑ ∑. 3n = (1 + 2)n =
k =0 k=0

∑. n kC(n,k) = n2n−1
k =1

:

kC(n,k) = nC(n − 1,k − 1)

nC(n − 1, 0) + nC(n − 1,1) + nC (n − 1, 2) + + nC (n − 1,n − 1)
= n[C(n − 1, 0) + C (n − 1,1) + + C(n − 1,n − 1)]
= n(1 + 1)n−1 = n2n−1

:

n n .
n
) 2n−1 n −1
. n2n−1
.(
k ,
.C (n, k )
k , .k

. kC (n, k )

∑. n kC(n,k) = n2n−1 , . n kC (n, k )
k =1
∑
n k =1

∑ (k + 1)C (n,k) ()

k=0