201Smt1_1061 - MACM 201 Test 1 February 6, 2006. 50 minutes...

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MACM 201 Test 1 February 6, 2006. 50 minutes Total marks: 45. Marks are indicated by ( ). N c 1 , ¯ c 2 ¯ c 3 ··· ¯ c t ) = N - [ N ( c 1 ) + N ( c 2 ) + ··· + N ( c t )] +[ N ( c 1 c 2 ) + N ( c 1 c 3 ) + ··· + N ( c 1 c t ) + ··· + N ( c 2 c 3 ) + ··· + N ( c t - 1 c t )] - [ N ( c 1 c 2 c 3 ) + N ( c 1 c 2 c 4 ) + ··· + N ( c 1 c 2 c t ) + N ( c 1 c 3 c 4 ) + ··· + N ( c 1 c 3 c t ) + ··· + N ( c t - 2 c t - 1 c t )] + ··· + ( - 1) t N ( c 1 c 2 c 3 ··· c t ) = S 0 - S 1 + S 2 - S 3 + ··· + ( - 1) t S t E m = S m - ± m + 1 1 ! S m +1 + ± m + 2 2 ! S m +2 - ··· + ( - 1) t - m ± t t - m ! S t L m = S m - ± m m - 1 ! S m +1 + ± m + 1 m - 1 ! S m +2 - ··· + ( - 1) t - m ± t - 1 m - 1 ! S t If n Z + , ± - n r ! = ± n + r - 1 r ! For all m,n Z + , a R , (1 + x ) n = ± n 0 ! + ± n 1 ! x + ± n 2 ! x 2 + ··· + ± n n ! x n (1 - x n +1 ) (1 - x ) = 1 + x + x 2 + x 3 + ··· + x n 1 (1 - x ) = 1 + x + x 2 + x 3 ··· = X i =0 x i 1 (1 + x ) n = ± - n 0 ! + ± -
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201Smt1_1061 - MACM 201 Test 1 February 6, 2006. 50 minutes...

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