(a) Prove the convergence or divergence of each of the following series: 1! +a! +3! + +n! 20+1 2+1 6 2²+1 23+1

Q: For which series monotone and bounded sequences theorem can be applied for the convergency? 2" a, =…

A: We have to find which series monotone and bounded sequence theorem can be applied for convergence.

Q: Determine whether each of the following series are absolutely convergent, conditionally convergent,…

A: As per the question we are given the following three infinite series : ∑ (-2)n² / (n + 2)! ∑ (-3)n…

Q: 2! .2 x. 3!3 5. 1+ 4! 2 32 3 4 54 + ... ∞

A: Given series is 1+x2+2!32x2+3!43x3+4!54x4+····

Q: (a) Use the binomial series to expand 00 3. 5:7. •(2n + 1) 5 + 5 ) x2n 2n. n! n = 1 1· 3· 5. *·(2n –…

A: Here by using the binomial series we have to expand  5/√(1-x2) .

Q: For which series monotone and bounded sequences theorem can be opplied for the convergency 2" a,…

A:

Q: Determine by ratio test the convergence or divergence of the series 1 19 2! 19 3! 3 4! 19 4 () 19 1+…

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Q: Use power series to show that 1 1 1 e =- + 0! +...** 2! 3! 4! 5! 6! 117

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Q: Determine whether the series is (are) converge(s) absolutely. 3* -1 A and D C and D None A and C

A: Solution is given as below:

Q: Determine whether the series 3⋅1!/1+32⋅2!/22+33⋅3!/33+…+3n⋅n!/nn+… converges or diverges.

A: Given series is 3·1·1!/1+3·2·2!/2·2+3·3·3!/3·3+…+3·n·n!/n·n To Determine : Whether the above series…

Q: 6- Test the convergence of the following series: 1 (2n + 1)3 n=1

A: Here we use limit comparison test .please see the explanation below.

Q: 4. Determine the convergence behavior of the series Σan for: (a) an √n+1-√n (b) an =(√n+1-√√n)/n…

A: This question is about sequence and series.

Q: Find the sum of the following series. 2" (a) En=0 Ση-03 m 3n n! 32 33 (b) 1+5 34 +. 4+54 2.52 3+53

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Q: (a) Prove the convergence or divergence of each of the following series: 1! 2! 3! (i) + + +. + n! 2n…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: (a) Determine whether the following series converges or diverges- (r!)³ (3r)! r=1

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Q: Prove that the binomial series a(a – 1) a (a- 1)... (а — п) + | | (1+ x)ª 1+ ax + 2! n! +...…

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Q: Which of the following series are convergent? I. 1+1/2² + 1/3² + ... 1/n² + ... II. 1 + 1/2 + 1/3 +…

A: The given series are; 1) 1 + 1/22 +1/32 +...+ 1/n2+...2) 1 + 1/2 + 1/3 +...+ 1/n+...3) 1 - 1/3 +…

Q: n² – 1 > Un where sn = u1 + ... + Un n² + 1 n=1

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Q: (a) Prove the convergence or divergence of each of the following series: 1! 2! 3! (i) + + 22 +1 + +…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: **** 22 use ratio test to determine if this series is convergent. 2 +++ determine the interval of…

A: We have to find the test of convergence and find the interval of convergence.

Q: 1. Describe the convergence of the series 3! + 3² + + (n+1)² (n + 2)! +

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Q: Determine whether the following series is convergent or divergent: 3 ola 2! O Divergent 3² 33 + 4!…

A: Given series is 32! - 324! + 336! - 348! + ...

Q: Check the convergence and find the sum of the series: 1 1 1 1 hint.: (2n – 1)(2n + 3) (2n – 1) (2n…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Using the I) Method of Successive Substitution, the II) Bisection Method, and the III) Regula-Falsi…

A: Given the function 3x=ex-sinx Find the root of the function in the interval 0,1 using Bisection…