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Calculus BC REVIEW Ch 8.1, 8.2, and 8.3 (Based on homework assignments). Calculators OK!!! 1. Write the first five terms of the sequence. an = 3n n! 2. Write the first five terms of the recursively defined sequence. a1 = 32, ak +1 = 3. Use a graphing utility to graph the first ten terms of the sequence. an = 1 ak 2 2 n 3 (2n − 1)! (2n + 1)! Determine the convergence or divergence. If the sequence converges, then find its 3n 2 − n + 4 limit. an = 2n 2 + 1 1 2 3 4 Write an expression for the nth term of the sequence. , , , ,... 2 ⋅3 3⋅ 4 4 ⋅ 5 5⋅ 6 Determine whether the sequence is monotonic. Discuss the boundedness of the 1 sequence. an = 4 − n 1 1 1 1 Find the first five terms of the sequence of partial sums. 1 + + + + ... 4 9 16 25 Graph the following sequence of partial sums, then determine the sum of the series. 4. Simplify the ratio of factorials. 5. 6. 7. 8. 9. ∞ 91 ∑ n =0 4 4 n ∞ 10. Verify that the infinite series converges. 1 ∑ n(n + 1) n =1 1 1 11. Find the sum of the convergent series. 3 − 1 + − + ... 3 9 12. Express the repeating decimal as a geometric series and write its sum as the ratio of two integers. 0.4 ∞ 3n − 1 13. Determine the convergence or divergence of the series. ∑ n =1 2n + 1 ∞ 14. Determine the convergence or divergence of the series. ∑ (1.075) n n =0 ∞ 15. Use the Integral Test to determine the convergence or divergence of the series. ∑e n =1 16. Use the Integral Test to determine the convergence or divergence of the series. ln 2 ln 3 ln 4 ln 5 ln 6 + + + + + ... 2 3 4 5 6 −n ∞ 17. Determine the convergence or divergence of the p-series. ∑ n =1 5 1 n 18. Determine the convergence or divergence of the p-series. 1 1 1 1 1+ + + + + ... 2 2 3 3 4 4 5 5 19. Approximate the sum of the convergent series using the indicated number of terms. ∞ 1 Include an estimate of the maximum error for your approximation. ∑ 2 Use ten n =1 n + 1 terms. ∞ 20. Find N such that RN ≤ 0.001 for the convergent series. ∑e n =1 −5 n