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Unformatted text preview: (a) X n =1 (-1) n 2-n ( n 2-1) n 2 + 1 . (b) X n =1 (-1) n n + 1- n n . (c) X n =1 x n n ! , where x is some real number. 7. Let X n =1 a n be a convergent series of positive terms. Prove that (a) if ( n N )( | b n | a n ), then X n =1 b n is absolutely convergent; 2 (b) X n =1 a n x n is absolutely convergent for-1 x 1....
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