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The Ratio Test Use the Ratio Test to determine whether the following series converge.
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Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
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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_forwardA FINAL EXAM TO BE COMPLETED INDEPENDENTLY. 13. Consider the four p-series listed below. Briefly explain whether each series converges or diverges. (a) 2n-1 no3 (b) 1n-4 1 (c) En 1 (d) E -1arrow_forward00 The series converge to n=1 (a)Ve - 1 (b) e - e4 (c)Ve - e3 (d) e?-1 (e) Nonearrow_forward
- Find the interval of convergence for the given power series. (x - 4)" Σ n(- 9)" n=1 The series is convergent from x = left end included (enter Y or N): to x = right end included (enter Y or N): M C ㅈ # $ A de L % 5 6 D 8 7 8 9 #arrow_forwardFind the intervalarrow_forwardchoices: a. true b. false c. others (specify) 1. Stationary series are series with roughly horizontal with constant variance. 2.A non-stationary series the ACF drops to zero quickly. 3. The PACF of the stationary series is decaying exponentially,arrow_forward
- Decide whether each series converges absolutely, converges conditionally, or diverges. 00 sin n The series (-1)"+6 ( - is ? n=1 (-7)"+6 is ? The series п+ 87 n=1 00 The series (-1)*+6 (47) is ? n=1arrow_forward12 Please help me with the answer and solution thank youarrow_forwardn3 Use the limit comparison test with the p-series to determine whether S 2n5 – 4n – 1 converges or diverges. n=2 The limit comparison test cannot be applied to these two series. S converges. S diverges. The test is inconclusive.arrow_forward
- Tests for Convergence 1. Consider the series Inn n=1 a. Use Comparison test to show that the series converges when p > 2 and diverges when p< 1.arrow_forwardan+1 Assume that an | converges to p = . What can you say about the convergence of the given series? %3D 00 bn n² an n=1 n=1 bn+1 lim b, (Enter 'inf' for .) E n a, is: n=1 A. convergent B. divergent C. The Ratio Test is inconclusivearrow_forwardDetermine whether the series is convergent or divergent. n=1 10-42-2 (-4)3n+1 The series ? Justification: (If more than one test is appropriate, pick the first applicable test in the list.) OA. This is a Geometric Series of the form > apr 1 n=1 OB. This is a Telescoping Series, lim s₁ = 12 00 OC. By the Divergence Test, lim an = T->00 OD. By the Direct Comparison Test, an ≤ bn with Σbn = Σc(), c = O E. By the Direct Comparison Test, an > bn where Σ bn = [c() where c = OF. By the Limit Comparison Test, let bn = c() where c = an lim n 100 bn f(x) dx = OI. By the Ratio Test, lim n 100 an+1 an where a = = OJ. By the Root Test, limno Van = OG. By the Alternating series test, i) {b} is ultimately decreasing because the function f satisfying f(n) = bn is decreasing on the interval ii) lim bn = n-00 = , P = OH. By the Integral Test, i) The function f satisfying f(n) = a₁ is positive, continuous, and ultimately decreasing on the interval fº and p = and its sum is and p = and (Enter "DNE" if…arrow_forward
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