4. Use the ratio test to determine whether or not the following series converges. (Hint: lim n→∞ (n + 1)² = e.) n 5. Show that the following series diverges. (Hint: lim cos n→∞ 1 n = 1.) ∞ nn Σ (2n)! n=1 Σtan (3) n=1

Q: 3 (8) ) (2n)! n=1

A: The given infinite series is: Let Ratio test for convergence of infinite series states that if…

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A:

Q: A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent.…

A: "Since you posted multiple questions, we will provide the solution only to the first 3 subparts of…

Q: Consider the following series. n = 1 Find the following limit. (If the limit is infinite, enter ''…

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Q: Q4. Use the Ratio or Root test to determine whether the following series converge. (2n)! (n!) ² ;…

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Q: 00 N(N+1) Consider the series > n. It can be shown that the Nth partial sum of this series is given…

A: topic - limits

Q: Determine the convergence or divergence of the following series. Σ n=0 n Vnt + 2

A: Here we will use integral test to check series is convergence or not .

Q: 1. In(6n) n4 - 2 3. n(In(n))2 %3D2 4. 1 5. nyn sin (4n) 6. n2 n=1 2.

A: We use different kind of series convergent set.

Q: 4"n! I (-1)". 9. 14 · 19 . (5n + 4) n = 1 dentify la,l. 4"n! (5n + 4)! 4"n! 9. 14 · 19 . (5n + 4)…

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