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Convergence or divergence Use a convergence test of your choice to determine whether the following series converge or diverge.
31.
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Calculus: Early Transcendentals (3rd Edition)
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- ✓ Q N For the series -e, determine which convergence test (if any) is the best to use. Select the correct answer below: @ O The alternating series test. The ratio test. The root test. O The limit comparison test. O None of the above. 2 W ∞0 Content attribution S X n=1 H command # 3 80 E D C $ 4 R F % 5 V T G ^ X6 MacBook Pro Y & 7 H U N * 00 8 J - M - 9 K O ) 0 < I H FEEDBACK 4 P A command را 0arrow_forwardt K Suppose a power series converges if |3x-6) ≤33 and diverges if |3x-615 33. Determine the radius and interval of convergence ICO The radius of convergence is R = Find the interval of convergence. Select the correct choice below and fill in the answer box to complete your choice OA. The interval of convergence is {x x=} (Simplify your answer. Type an exact answer.) B. The interval of convergence is (Simplify your answer. Type an exact answer Type your answer in interval notation.)arrow_forwardUsing the Direct Comparison Test or the Limit Comparison Test determine if the series converges or diverges.arrow_forward
- 00 Consider the series (-1)"(7x+ 2)". n=0 (a) Find the series' radius and interval of convergence. (b) For what values of x does the series converge absolutely? (c) For what values of x does the series converge conditionally? EAL WITH CAUTION HE PRODUCT AWAY UABLE ITEMS cay dặc o các loạn với bữa (a) Find the interval of convergence.arrow_forwardUse the binomial series to expand the function as a power series. 9 (4 + x)3 ∞ n = 0 State the radius of convergence, R. R =arrow_forward00 Does the seriesE(- 1n+12+n° n4 converge absolutely, converge conditionally, or diverge? n= 1 Choose the correct answer below and, if necessary, fill in the answer box to complete your choice. O A. The series converges absolutely per the Comparison Test with > 00 n4 n= 1 B. The series diverges because the limit used in the Ratio Test is not less than or equal to 1. OC. The series converges conditionally per the Alternating Series Test and the Comparison Test with n= 1 D. The series converges absolutely because the limit used in the nth-Term Test is E. The series diverges because the limit used in the nth-Term Test does not exist. O F. The series converges conditionally per the Alternating Series Test and because the limit used in the Ratio Test isarrow_forward
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