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Unformatted text preview: ; ( r f ) = r f if r ∈ R ; ( f g ) = f g + f g ; ( f n ) = n f n − 1 f for all n ≥ 1 . Solution. Let f ( x ) = ∑ a n x n and g ( x ) = ∑ b n x n . (i) ( f + g ) = ³ X a n x n + X b n x n ´ = ³ X ( a n + b n ) x n ´ = X n ( a n + b n ) x n − 1 = X na n x n − 1 + X nb n x n − 1 = f + g . (ii) ( r f ) = ³ r X a n x n ´ = ³ X ra n x n ´ = X rna n x n − 1 = r X na n x n − 1 = r f ....
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This note was uploaded on 12/21/2011 for the course MAS 4301 taught by Professor Keithcornell during the Fall '11 term at UNF.
 Fall '11
 KeithCornell

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