Determining Convergence or Divergence In Exercises 27-34, test for convergence or divergence, using each test at least once. Identity which test was used.
(a) nth-Term Test
(b) Geometric Series Test
(c) p-Series Test
(d) Telescoping Series Test
(e) Integral Test
(f) Direct Comparison Test
(g) Limit Comparison Test
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Chapter 9 Solutions
CALCULUS EARLY TRANSCENDENTAL FUNCTIONS
- 1 Σ In which case is the convergence test that should be used to determine the character of the series and the result to be reached correctly? n. Inn n=2 (a) Integral Test is used; series is convergent (b) Integral Test is used; series is divergent (c) E Comparison (Direct Comparison) Test is performed with the series, the series n° is convergent n=2 (d) Comparison (Direct Comparison) Test is performed with the series; series is 3 n=2 divergent (e) The Ratio Test is used; series is convergentarrow_forwardStudy the power series: - Using Limit Comparison Test show that this series converges when x = -2. - Justify if the series is absolutely convergent, conditionally convergent, or divergent at x = 12? - Determine the radius and interval of convergence of the power series. (5-x)" Σ n=27 √√n5-9arrow_forward(-1)" (b) Test: diverges converges 2n n=0 Reason: (e) * (1+ 4)" Test: diverges converges n=1 Reason:arrow_forward
- USING ALTERNATING SERIES TEST PROVE THAT THIS CONVERGES.arrow_forwardcourse : real analysisarrow_forwardtan-ln | Consider the series n² +1 n=1 Is it true that the Integral Test can be used to determine the convergence or divergence of this series? [ Select ] Is the series convergent or is it divergent? [Select ]arrow_forward
- Example Test the series for convergence or n=1n3+1 divergence.arrow_forwardTest the series for convergence or divergence using the Alternating Series Test. (-1)" - 1 In(4n + 3) n = 1 Identify b, Evaluate the following limit. lim b, n-00 Since lim b.? 0 and b. +1 b, for all n, ---Select--- n-00arrow_forwardSeries Condition 9arrow_forward
- Series Ror being Convergent the Pollo wing Series divergenk Test or e " 1+ earrow_forwardAlternating Series Test. Find if converging or diverges by the first derivative processarrow_forward(- 4)" Consider the power series > An(x + 6)" where An = n! that is, the series n=0 ( – 4)" (x + 6)" - n! n=0 (a) What is the centre of the power series? An+1 (b) Evaluate lim An (c) What is the radius of convergence for the given power series? (Enter in a fraction or number rounded to three decimal plac oo for o, -oo for – o, or DNE.)arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage