Use the Ratio Test to determine whether the series is convergent or divergent. Identify an Since lim 00 n→ 00 n = 1 Evaluate the following limit. lim n→ 00 n 30 a 'n +1 +1 an ? 1, ---Select---

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For each set of conditions below, give an example of sequences/series that satisfy the conditions (and show that they do), or explain why the sequence/series cannot exist. (a) A sequence {an} that is not monotonic, but converges to the limit 2021. (b) A series > a, that can be shown to converge using the Integral Test, but not the Ratio Test. 00 (c) Two different series > An and bn that converge to the same sum, and another series ) Cn that diverges, n=1 n=1 n=1 such that an < Cn < bn for all n.

Consider the series E, an where an = (-1)"(mM) yn In this problem you must attempt to use the Root Test to decide whether the series converges. Compute L = lim Vlan| n-00