What is the value of p = lim+¹ when applying the Ratio Test to assess n→∞an a convergence of? What is the conclusion of the test? n=134 A. 1; test is inconclusive B. 0; convergent C. 0; divergent D. ~; divergent

8. 2. Let an be convergent with an > 0 for all n. Now consider (an). n=1 n=1 a) Explain in words why it must be true that (an)2 < an for sufficiently large n. b) Does (an)² converge or diverge? Explain in words and be sure to cite a test n=1

Use the Integral Test to prove the p-series Test : k=1 1 NP is convergent if p > 1, divergent for ≤ 1. State the integral test first and check if the function satisfies all the required conditions before applying the integral test.

n³x" Determine the radius and interval of convergence: En=15

Use series development to determine the threshold value.

Use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integral for convergence. If more than one method applies, use whatever method you prefer. J In |지 dk -3 ... Choose the correct answer below. O A. By integration, the integral has a finite value, so the integral converges. O B. By integration, the integral does not have a finite value, so the integral diverges. f(x) is not a finite limit. g(x) By the Limit Comparison Test, the integral diverges because lim x00 OD. - 3 By the Direct Comparison Method, the integral converges because In |x| dx converges and In |x| dx converges. - 00 3

Prove convergence or divergence.

is the suquence converge or diverge. Explain in detail your answers.

Determine convergence or divergence using any method covered so far.

tan(3/2") 2 SELECT A A) converges B) tan(3/2") 2 hint: tant = tan(3) %3D tant tan(2t) n-0