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_forwardDetermine whether the sequance in images is convergent ( find the value it convengers), divergent, divergent to ∞ or -∞ for any fixed k≠0arrow_forwardThe test for DIVERGENCE says: If lim ak does not exist or is not equal to 0 the series E ak is divergent k=1 If lim ak exist, the series 2 ak is convergent k=1 If lim ak is equal to 0 the series E ak is divergent k=1 If lim ak is equal to 0 the series 2 ak is convergent k=1arrow_forward
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- 4. (P14, Page 34; i ) Prove that the sequence {sn} converges to 1 where {sn} is defined by 1 1 + 3- 2 1 for every index n. + (n + 1)(n) Sn = 2.1 1. (Hint: first simplify sn by using 1 1 and then apply properties of convergent sequences. You can k +1* (k + 1)k k 1 use the fact that lim = 0 without proof.) n+0 n + 1arrow_forward(k + 1)'/2 (k5 + k3 – 1)/3 1. Show that converges. k=1arrow_forward1. (a) State whether the sequence {an}, with an defined below, converges or diverges. If convergent, find the limit of the sequence. Provide justification for your answer. an = /9n - 4 4n+1 (b) Consider the series an where an is defined in part (a). Use your answer to part (a) to conclude whether this series converges or diverges. Support your answer by referring to a specific result or test discussed in class.arrow_forward