(a) Prove the convergence or divergence of each of the following series: 1! 2! 3! n! (i) + + +. + + 2+1 2² +1 23 +1 2n + 1 1 1 + 1 3 + (−1)n-1 2n 1

Q: By recognizing each series below as a Taylor series evaluated at a particular value of z, find the…

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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: 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: 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: Use the formula for the binomial series: (1 + x)" = 1+ тx + 2! m(m–1)2 + m(m-1)…(m-k+1) k1.. ... k!…

A: 1 + xm = 1+ mx + ∑k - 2∞m(m - 1)(m - 2) ... (m - k + 1)k!xk if x <1 is the binomial expansion. We…

Q: Use the formula for the binomial series: (1 +x)" = 1+ mx + + + -1) %3D = I+ Ei to obtain the…

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Q: Show that the following series is not absolutely convergent 1+k² (-1)*. 2-k km3

A: As per our company guideline we are supposed to answer only first  qs, kindly post remaining qs in…

Q: . Determine if the following series is convergent or divergent (−1)n+1n² n³+4 b) Σ=1 Σn=1 700 a)…

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

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Q: Consider a series En-1 an where (an)n is a monotonically decreasing sequence of non- negative real…

A: It is given that the sequence  is monotonically decreasing sequence and  for all  and it is…

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: Find the first few nonzero terms of the Maclaurin series for the given function. f(x) - In(1-3x)…

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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: Use the formula for the binomial series: (1 + x)" = = to obtain the Maclaurin series for (k + 7)! 1…

A: Please see the attachment  4th option is correct

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: (a) Expand 9 1 + x as a power series. 00 09-2x+9 ○ 9 - 00 n = 0 9 - 00 9 -x+ n = 2 00 + 1)! -x"…

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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: f(x) = xsinx (-1)"x2n (2n+2)! .2n+2 OA. (-1)"r2n+2 (2n + 1)! O B. n=1 (-1)"x2n+1 (2n+ 1)! C. 1.…

A: Maclaurain series

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

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Q: Which one of the following series is divergent? 1 1 (A) E (B) E 2n + n + 1 n2 + Vn n=1 n=2 1 (C) E…

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

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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…