UIZ # 6 Problems 1. Calculate the first 10 terms (starting with n=1 ) of the sequence a1=2, a2=2,, for n3, a n=a n1 an2 2. State whether the sequence converges or diverges? If the sequence converges, find its limit. 3n 2 2n 4 2 2n 2 2 n 1 3. Does the series definitely diverge by the nth Term Test? If not, what can we conclude? 8n 4 3n 2 5n 2 4 3 2 n 1 4 n 2 n n n 3 4. Rewrite the geometric series using the sigma notation and calculate the value of the sum. 3 9 27 81 1 5 25 125 625 5. Find all values of x for which the geometric series converges and find its sum. 2 x 3 k k 0 6. Calculate the value of the partial sum for n=4 of s n as n approaches infinity. 1 1 k 2 k 1 k 3 and n=5 and then find the limit 7. Use the Integral Test to determine whether the following series converges or diverges. Solving using other methods will not be credited. (a) (b) k 1 1 3k 2 k 0 k 2k 4 k 1 e 8. Use the Comparison Test or the Limit Comparison Test to determine whether the given series converges or diverges. Solving using other methods will not be credited. (a) (b) (Hints: ) 1 sin x 1 3 sin k k 2 2k 1 3 4k 2 k 1 k 1 5k k 3