Select between converges or diverges to fill the first blank.
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- Determine whether the sum of the infinite series is defined. 24+(12)+6+(3)+arrow_forward00 4" converges or diverges. (9n)2 t) Use the ratio test to determine whether >. n=6 d the ratio of successive terms. Write your answer as a fully simplified fraction. For n > 6, 324n^2 аn+1 lim an (9n+1)^2arrow_forwardIV.) 1. Convergent or Divergent series will give upvote if correctarrow_forward
- b) Determine whether the geometric series (-1)"-15n-1 00 n=1 6t" is convergent or divergent, and if it is convergent, then find its sum. Find also the partial sum Sm and its limit as m → 0. Discuss your findingsarrow_forwardConsider the series San where n=1 (-1)"n n² + 2n + 5 In this problem you must attempt to use the Ratio Test to decide whether the series converges. Compute an = an+1 L = lim n-00 an Enter the numerical value of the limit L if it converges, INF if it diverges to infinity, -INF if it diverges to negative infinity, or DIV if it diverges but not to infinity or negative infinity. L = Which of the following statements is true? A. The Ratio Test says that the series converges absolutely. B. The Ratio Test says that the series diverges. C. The Ratio Test says that the series converges conditionally. D. The Ratio Test is inconclusive, but the series converges absolutely by another test or tests. E. The Ratio Test is inconclusive, but the series diverges by another test or tests. F. The Ratio Test is inconclusive, but the series converges conditionally by another test or tests. Enter the letter for your choice here:arrow_forwardWk4 2arrow_forward
- an -0 and Show that if lim %3D =1 n+ 00 converges thenEn=1 'n =1 converges too.arrow_forwardApply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is inconclusive. 00 5n? (2n + 1)! n=1 p = lim = an+1 (Enter 'inf' for .) an 00 5n2 is: (2n + 1)! n=1 A. convergent B. divergent C. The Ratio Test is inconclusivearrow_forwardplease send correct answer Q5arrow_forward
- 6. (a) Show that sinh (r) = cosh(2.r) – 1 2 (b) Find the nth term of the following sequence {1,8, 10, 26, 46, -..} for all n 2 1. (c) Define both absolute convergence and conditional convergence of a series. 7. (a) Given a,+1 = 2a, + an-1 and b+1 = 2b, + bn-1 for n 2 1, with ao = a1 = 1 and bo = 0, bị = 1. It can be shown that (1+ v2)" = an + b, V2, Vn 2 0. Hence, prove %3D !! that a - b = (-1)". 2 - VA-x (b) i) Compute lim ii) Hence prove the limit in i) above by e-d definition.arrow_forward(-1)" is which of the following. (circle one...you can show work for partial 8. The series n=1 credit) (a) Absolutely convergent (b) Conditionally convergent (c) Divergentarrow_forward2k-1 3. Determine whether the series 2 is convergent k+4 k = 1 or divergent by the Kth - Term test ? Divergent. А. Convergent В. Conditionally connvergent С. Cannot be determined. D.arrow_forward