Assignment 1

Assignment 1 - Mathematics 222 Assignment 1 1 1. Does the...

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Mathematics 222 Assignment 1 1. Does the sequence b n = sin( π 2 + 1 n ) converge or diverge? If it converges, what is the limit? 2. Does the sequence b n = cos( ) converge or diverge? If it converges, find the limit. 3. Does the sequence b n = n 2 (1 - cos( 1 n ) converge or diverge? If it converges, what is the limit? 4. Does the sequence b n = 1 n 2 - 1 - n 2 + n converge or diverge? If it converges, find the limit. 5. Test the following series for convergence (absolute or conditional) or di- vergence justifying your answer X n =1 ( - 1) n +1 1 + n n 2 6. Test the following series for convergence (absolute or conditional) or di- vergence X ( - 1) n +1 ( n !) 2 (2 n )! 7. Test the following series for convergence (absolute or conditional) or di-
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