6) a) Σ k=1 Determine whether each of the series below converges or diverges and explain your reasoning (k!)³ (3k)!

Q: (b) Prove that the real power series n!r" converges for only r 0. %3D

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Q: 00 6" +3 2(-1)"-b,, where b,=- n' n n=1 (n+3) 9"+4 a) Find and simplify bn+1 bn b) Test the given…

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Q: Which series given below converge conditionally. (-1)" n=2 n²+1 (-1)" 2 Inn 1) E-2 00 II) E, (-1)"…

A: For details solution see the  answer below

Q: Work Problem .. Question 1 2-. a) ]: Show your work. <]: Determine whether the series 1 Σ n=1…

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Q: convergent serie 12) Find the sum of each 2 A) / + = + ( ² ) ² + ( ² ) ³ + ( ²1 ) 4 + ... ( - )^² +…

A: Let's find sum of given series.

Q: 8 (iv) [(-1) n=1 n :)" sin n n+1 [ Select] [Select] is conditionally convergent is divergent. is…

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Q: (3x - 1)" n Consider the power series a) Show that the resulting series when r = 0 is conditionally…

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Q: Let {cn} be a positive, increasing sequence such that lim cn = 2. Determine whether the following…

A: Given that                                             limn→∞cn=2

Q: 1)Which of the series given below converge absolutely? Conditionally converges? Divergent? Explain…

A: It is given that the series ∑n=1∞-1n+1nn2+1. Check the series ∑n=1∞-1n+1nn2+1 is absolutely…

Q: Consider the power series 80 an (x – 6)" n=1 of variable x and with (a some sequence. If it is known…

A: In this series we have to find whether the series is convergent of divergent.

Q: Question 8 k k Determine whether the series>(G) k +7 converges or diverges. a) Odiverges b) cannot…

A: We know that by general necessary condition of convergence of series

Q: 2) What are all values of p for which the infinite series (A) p > 1 (B) p> 2 (C) p≥ 2 n +1…

A: The given series is summation of n/(np+1), n from 1 to infinity.

Q: k! (ii) ek k=1

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: (-1)* k2 the series by adding together the first 10 terms. What is the maximum error or a) Consider…

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Q: n=1 (n!)² (kn)!

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Q: Q4) Determine whether the series is convergent or divergent. 1 a)Sw=15 7n2-13n+9 nt+16 b)Σ=17…

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Q: Q2/ A) Determine if the following series is convergent or divergent 2n En=1 3n n! n! En=1 (2n) 00

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Q: 00 16n+3 E(-1)"-1. n²+3 n – | n=1 a) Determine whether or not the series is absolutely convergent.…

A: This is a problem related to series and sum calculation. Based on the general formula and concepts…