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# final - Math 9C Final exam Study guide C Pro Fall 2011 1...

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Math 9C Final exam Study guide C. Pro - Fall 2011 1 Concept questions What is the difference between a sequence and a series? Can you give the definition of what it means for a sequence to converge? What is the definition for a series to converge? If the a k ’s are nonnegative, why does this say the sequence of partial sums is an increasing sequence? What is the Monotone bounded convergence theorem? Can you explain how the integral test is used to show your sequence of partial sums is bounded? How did we come up with the p -test? How are the integral test and the comparison test similar? 1.1 Sample Problems State the integral test, comparison test, limit comparison test, alternating series test, ratio test, and root test. Find the n -th term of the sequence { 1 , 0 , 1 , 0 , 1 , 0 , . . . } Find the limits as n → ∞ of the following sequences • { 3 1 /n } • { 4 n 2 +2 n 3 +3 } • { 1 2 n } • { n n } Hint: n n = e ln( n ) n (Do you know why?) • { n sin 1 n } • { n ln ( 1 + 1 n ) } Hint: L’Hospital’s rule.

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