Page 159 - Fixtures
P. 159
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[AIME 1986] ( )
1 − x + x2 − x 3 + + x16 − x17 )
a0 + a1y + a2y2 + + a16y16 + a17y17
)
a2 ai ,y = x + 1 )
[AIME 1991] ( )
(1 + 0.2)1000
(1 + 0.2)1000 = C (1000, 0)(0.2)0 + C(1000, 0.2)1
+C (1000, 2)(0.2)2 + + C(1000,1000)(0.2)1000
= A0 + A1 + A2 + + A1000
k .k = 0,1, ,1000 , Ak = C(1000,k)(0.2)k
P0(x) = x 3 + 313x2 − 77x − 8 Ak
.n ≥ 1 [AIME 1993] (
Pn (x) = Pn−1(x − n)
P20(x ) x
n [AIME 1996] (
. 1996 (xy − 3x − 7y − 21)n
[AIME 2000 II] (
1+1+1+1+1
2 !!× 17 ! 3 !!× 16 ! 4 !!× 15! 6 !!× 13! 7 !!× 12 !
+1 + 1 = n
8 !!× 11! 9 !!× 10 ! 1!!× 18 !
n
100
