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MATH 152 Activity 11 (Section 10.4) Directions: Put both your name and your partners name on the answersheet. Use scratch paper for work, meaning only put the answers on the answer sheet. Turn in only ONE answer sheet per pair. Calculators are allowed and you may use your notes and textbook. Failure to follow these instructions will result in a 1 point deduction. Neat handwriting is expected. 1. Does the series ∞ X (−1)n converge or diverge? Name the test you applied. n2 + n n=1 2. Does the series ∞ X (−1)n n2 converge or diverge? Name the test you applied. n + n2 n=1 ∞ X an+1 (−3)n = , we find that lim 3. If we apply the ratio test to the series n (n + 1) n→∞ 5 a n n=1 and therefore the series . ∞ X an+1 (−1)n = , we find that lim 4. If we apply the ratio test to the series n (n + 1)! n→∞ 5 a n n=1 and therefore the series 5. If we apply the ratio test to the series and therefore the series . ∞ X an+1 (2n + 1)! = , we find that lim n→∞ an 7n (n!)2 n=1 . 6. Does the series ∞ X (−1)n converge absolutely? Name the test you applied. n2 + n n=1 7. Does the series ∞ X (−1)n converge absolutely? Name the test you applied. (n − 1) ln(n − 1) n=3 8. Use s6 to approximate ∞ X (−2)n and give an upper bound on the error. (2n + 3)! n=1 1