Q6) Test the convergence of the following (n+1)(n+2) 1) Σ=1 n! n! 2) Σ=1 3) En=1 (2n+1)! (n!)" · (nn)2

Q: Does (-e)³n! (2n)! (3n)! n=1 converge absolutely, conditionally, or not at all? Justify your answe

A: The series is .To Find:Does the series converge absolutely, conditionally, or not at all?

Q: 2+ Sinno al) E

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Q: Which of the following series is conditionally 1 A) B) (-1)" Vn2 n-1 n=1 C) D) (-1)n+1 n3 +1 n-1 n=1…

A: The objective is to tell which series is conditionally convergent in the given series.

Q: 10 Prove whether the series converges or diverges. cos(nn) a) E 2n-1 b) Σ c) E '(n!)² (2n)!

A: By ratio test and Lebinitz test we can give the answer for both questions.

Q: 8!x2 1+ 4!x + 12!æ3 16!æ4 20!25 + + .. (2!)4 (3!)4 (4!)4 (5!)4 R = (If the radius is infinite, enter…

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Q: which of the following SSeries Converge 7n 2n2+1, tan

A: Series and sequences

Q: 8 n1² Σ (2η)! n=1

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Q: Q1 Test the convergence of the series Σ=o(−1)n+1 (n!)² (2n)!

A: Given series is convergent. Explanation is as follows

Q: En=1 (-1)^(n² + 1) 4 n

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Q: 8. Determine if the series diverg (-1)" a) /2n2-2 n=0 |

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Q: -1) (x-2)* (k+1)3ª х — The series has radius of convergence 3. The interval of k=0 convergence of is…

A: Interval of convergence I=

Q: 12. Determine Converges a) = cos(n) which of the following series. b) = 1=1 c) 32² d) [(+)² 7-1 3 n

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: The interval of convergence of the series CO (x - 4)" 2n n +4 n=0 is: (2, 6]. (2,6). [2, 6). A) B)…

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Q: Find the interval of convergence of the power series

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Q: Test the convergence of the following: n 3n+1 1- an 3n-1

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Q: Test the convergence of the series 2n2 3n²-4n n=1 sin r Evaluate lim 1-0 r3 – 2x

A: Let's find.

Q: Consider the following convergent series: too 11 11 n+1 23 + k 23 + k n-2 with k a real constant…

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Q: Test for convergence, Mceegobams Ka Q n! (2nH)! (3n)!

A: Here we will check the convergence of the given series.

Q: P1 (a) Use the integral test to study the convergence of the series Is it absolutely convergent? ∞…

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Q: 29. Which of the following is a power series expansion of 6 X 2n X x (A) 1 + + + + + 2! 6! (2n)! 6 X…

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Q: 00 A) > n! x" is convergent for x = n=1 00 B) E n! (10x – 8)" is convergent for x = n=1 C) The…

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Q: Prove the conditional convergence ofR = 1 +1/2 +1/3 − 3/4 +1/5 +1/6 +1/7 − 3/8 +···

A: Consider the given:…

Q: . Prove that the interval of convergence of the series Σ (-1)*--," 71 1. is -1<r <1.

A: See the attachment

Q: 3. Determine which of the fol 2" (a) n=1 n! (d 1 (b) (e n=1 2n 3n n+1 (c) (E 3n n=1

A: Since you have posted multiple questions i can do first three subparts as per our company guidelines…

Q: k=1 k 2k + 1 k

A: Given series is∑k=1∞k2k+1k . Since the series is positive term series so we can apply Cauchy nth…

Q: 3" n=1

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Q: What a n' 6) Σ-r 2" abso n=1 conver conditi

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: (2n)! Σ n2n converges n = 1 Select one: True False

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Q: 2n + n n! S. In2 + 4n + 1 2" ( 2n2 + 2n + 4 n2 + 4n +1

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…