Page 62 - Numbertheory

@ @Hßìÿa@ö§aI@†a‡Èÿa@óî‹Åä@@

[AMC10B 2006] ( )

S = 7!+ 8!+ 9! + ... + 2006!

6( ) 4( ) 3( ) 1 ()

100 n! : ( )
. n ≥ 10

10 ! +11! + ... + 2006 !

7! + 8! + 9! = 5040 + 40320 + 362880 = 408240 . 00

.4 ( S )

<n > [AMC10A 2008] ( )

<<< 6 >>> .n n 6 ()
24 ( )
32 ( ) 12 ( )

< 6 > =1+ 2+3 = 6 : () )
<< 6 >> = < 6 > = 6 [AHSME 1971] (
<<< 6 >>> = < 6 > = 6

70 60

248 −1

65 61 ( ) 63 61 ( )
67 63 ( ) 65 63 ( )

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