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BC 3 Sequences and Series Quiz No Calculators allowed. Show set-up/method clearly on all problems. #1. Name: Complete (no work necessary): a a. An expression of the form k 1 k is called an . Corresponding to this, we have the sequence {Sn}, which is called the . The nth term of this sequence is given by Sn = The sequence {an} is called If lim(an ) 0 then . . . n b. The series ar k converges to if and only if <r< k 1 c. Root Test: If lim n L , , and a , then k 1 #2 (2 pts each) Look at the series k converges. n k 1 k 1 ak . Let Sn ak n 1 for all n 1. . n a. Find a1 , a2 and a3 . b. Determine whether a k 1 k converges or diverges. If it converges, find the sum. #3(6 pts each) Determine whether each series converges or diverges. Explain reasoning carefully and completely. a. b. 3n 2 n n 1 n 2 2 1 n n 1 c. tan n 1 n 2 2 1 ( n) #3 (continued) Determine whether each series converges or diverges. Explain reasoning carefully and completely. n ! n n n 1 (2n)! d. 1 1 approximates the value of k k k 1 k 5 k 1 k 5 with an error less than .001. You need only find the value of n, not S n . Explain your reasoning clearly. n #4(6 pts) Find a value of n such that S n #5 (3 pts) Evaluate the sum 3k 5 k 1 k .