# T2 - A x and B x be series(a Using the usual rules from...

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Problem 1: Compute the following: a) [ x n ] 1 (1 - 5 x 4 ) 3 ; b) [ x n ] (1+ x ) 2 (1 - x ) 5 . Problem 2: Prove that r + s = t ( - 1) r ( n + r - 1 r )( m s ) = ( m - n t ) by computing [ x t ] (1+ x ) m (1+ x ) n and [ x t ](1 + x ) m - n . Problem 3: Prove that (1 + x ) 7 n (1 + 3 x ) 13 = k 0 k i =0 ( 7 n i )( 13 k - i ) 3 k - i x k . Problem 4: A travel agency has a limited number of six diﬀerent pamphlets about the Caribbean Islands. The agent requests that you take at most 7 pamphlets and not more than two of any one kind. How many choices can you make? Problem 5: Let
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Unformatted text preview: A ( x ) and B ( x ) be series. (a) Using the usual rules from Calculus, show that ( A ( x ) B ( x )) = A ( x ) B ( x )+ A ( x ) B ( x ). (b) Assuming that [ x k ] A ( x ) = a k and [ x k ] B ( x ) = b k , compute formulas for the coeﬃcient of x n in ( A ( x ) B ( x )) and in A ( x ) B ( x ) + A ( x ) B ( x ) and check that they are the same. 1...
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## This note was uploaded on 11/26/2011 for the course MATH 239 taught by Professor M.pei during the Spring '09 term at Waterloo.

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