Page 160 - Fixtures

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10 i [MAΘ 1992] ( )
[MAΘ 1992] ( )
∑ ∑C(i,k)
)
i=1 k =1 )

44C(45, 0) + 43C(45,1) + 42C(45,2) + )
)
.(2a −b + 3c − 5d)10 + 0C(45, 44) −C(45, 45) )

(

n(

C(n,1) + 3C(n, 3) + 5C(n,5) + + (n − 1)C(n,n − 1)

= n2n−2

. n − 1) = C (2n,n − 1) (

∑C (n,k)C(n,k
k =1

∑. n k 2C (n,k) = n(n + 1)2n−2 (

k =1

[AIME 1992] (

3:4:5

n ()
()
∑ iC (i − 1,k − 1) ()
()
. i=k

C (n, k )

. k (n, i )C (n − i, k − i) = 2kC (n,k)

∑C
i=0

. n (n, k )C (n, n − k + 1) = C (2n,n + 1)

∑C
k =1

.[( ) : 20

∑C (20,k)C (20,k − 1)]
k =1