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HW 03 - gonzales(pag757 HW 03 Odell(57000 This print-out...

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gonzales (pag757) – HW 03 – Odell – (57000) 1 This print-out should have 23 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points If a n , b n , and c n satisfy the inequalities 0 < a n c n b n , for all n , what can we say about the series ( A ) : summationdisplay n =1 a n , ( B ) : summationdisplay n =1 b n if we know that the series ( C ) : summationdisplay n =1 c n is convergent but know nothing else about a n and b n ? 1. ( A ) need not converge , ( B ) converges 2. ( A ) converges , ( B ) need not converge 3. ( A ) diverges , ( B ) converges 4. ( A ) converges , ( B ) diverges 5. ( A ) converges , ( B ) converges 6. ( A ) diverges , ( B ) diverges 002 10.0 points Which, if any, of the following series converge? ( A ) summationdisplay k =2 1 k (ln k ) 2 + 3 ( B ) summationdisplay n =5 parenleftBig 2 3 parenrightBig n 1. B but not A 2. A but not B 3. neither A nor B 4. A and B 003 10.0 points Determine whether the series summationdisplay n =1 3 6 + 4 n converges or diverges. 1. series is divergent 2. series is convergent 004 10.0 points Which, if any, of the following series converge? ( A ) summationdisplay n =4 4 n n - 3 ( B ) summationdisplay n =1 1 + sin n 3 n 1. A but not B 2. B but not A 3. neither A nor B 4. A and B 005 10.0 points Determine whether the series summationdisplay k =1 ( - 1) k - 1 cos 2 k 4 k
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