Unformatted text preview: K 1 ,K 2 ∈ N such that  a nA  < ± 2 , ∀ n ≥ K 1 ,  b nB  < ± 2 , ∀ n ≥ K 2 . Take K := max { K 1 ,K 2 } . We have  a nA  +  b nB  < ±, ∀ n ≥ K ( ** ) . By combining ( * ) with ( ** ) , we obtain that, for any ± > , there is K ∈ N such that  ( a n + b n )( A + B )  < ±, ∀ n ≥ K, that is, we have showed that ( a n + b n ) → ( A + B ) . 1...
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 Fall '10
 Mark
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