Question

1. Write down the first few terms of a sequence. How to determine if a sequence is convergent or divergent? 2. Write down the first few terms of a series. Partol sus 3. Tests to determine if a series is convergent or divergent. Divergent Test, Geometric Series Test, Telescopic Series Test, Integral Test, p-series Test, Comparison Test, Limit Comparison Test, Ratio Test, Root Test, Alternating Series Test 4. How to determine whether a series is geometric and whether it is convergent or divergent? If a geometric series is convergent, what is its sum? 5. How to find the sum of a telescopic series? 6. What are p-series? How to use p-series in applying Limit Comparison Test? 7. Do you really know how to apply the Ratio Test? 8. What is the difference between absolute convergence and conditional convergence in alternating series? 9. What is a power series and how to find its radius and interval convergence? Around x 0 vs around x a? 10. What is the difference between a Taylor series and a Taylor polynomial? 0 vs around x = a? 11 , How to construct the Taylor series of a function? Around x 12. How to use substitution, addition, subtraction, multiplication, division, differentiation, and integration to create new Taylor series from some known Taylor series? 13. How to use Taylor polynomial to approximate a value of a function?

Answer 1

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