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Unformatted text preview: S ( x ), as a product of polynomials, so that [ x k ] S ( x ) counts the number of ways of choosing k marbles under the condition that the total number of red and green marbles chosen is odd. 3. (4 points) Suppose that the formal power series A ( x ) = a + a 1 x + a 2 x 2 + satises the equation (1 + x + x 2 ) A ( x ) = 3 + 5 x 2 . By considering the coecients of x , x 1 , x 2 , and x 3 on either side of this equation, determine a , a 1 , a 2 , and a 3 . 4. (8 points) (a) Using Theorem 1.8.2, show that (1-4 x ) 1 2 = 1-2 x X k 1 k + 1 2 k k ! x k . (b) Using the Binomial Theorem (Theorem 1.8.1), show that (1-4 x )-1 2 = X k 2 k k ! x k ....
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This note was uploaded on 08/13/2011 for the course MATH 239 taught by Professor M.pei during the Spring '09 term at Waterloo.
- Spring '09