Consider the series Suppose T-1. lim ky00 TL1 (2₁(-1²) CT CH() X Hint: Consider what happens if k is odd and if k is even.

Does the sequence {a,} converge or diverge? Find the limit if the sequence is convergent. 2. 1 sin 6n - 1 Select the correct choice below and, if necessary, fill in the answer box to complete the choice. O A. The sequence converges to lim a, = |- (Simplify your answer.) O B. The sequence diverges.

Let r = 14. For both of the following answer blanks, decide whether the given sequence or series is convergent or divergent. If convergent, enter the limit (for a sequence) or the sum (for a series). If divergent, enter INF if it diverges to infinity, MINF if it diverges to minus infinity, or DIV otherwise. A. Consider the sequence {nr"}. lim nr² = n→∞0 B. Take my word for it that it can be shown that Now consider the series Σ n=1 nr. = n=1 nr. iri ² − (n + 1)pn+¹ + r (1-r)² npr+2

Let a, = 2" cos(n7) for n21. Write out the first 8 terms of the sequence (a, through ag). Determine lim a, . Note: You must show all your work and justify your steps carefully. а. b. Determine if Ea, converges (absolutely or conditionally) or diverges. Note: You must show с. all your work and justify your steps carefully.