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

Q: Find the sum of the series n (r +1) (n+2)* 32 (n +3*) 3/2 as n → 00_ n +(n-1)| 3/2

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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: 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: 8 n1² Σ (2η)! n=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: 5) Evaluate the following infinite series exactly. 10, 20. 40 а) 5+—+ 3 9 27 27 81 243 -+=+: 5! b)…

A: Please see the answer below.

Q: Using the first five terms of a sequence formed by (3n - 2), what series will be formed?

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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: verify that the series diverges

A: Step 1: Step 2: Step 3: Step 4:

Q: 1.7 Show that 1² +2²+ +n² -1 n(n +1) (2n + 1).

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

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Q: n + 3 2n + 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: Find the Maclaurin series for the given function. A) B) 6+z (-1)"z*+1 6 (-1)"z" o 6+1 D) (-1)"z"…

A: In this question we have to find the Maclaurin series of the function.

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: Which of the following sequence is divergent? en {"} (-1)*+1 n s n² In+1 } {-3}

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Q: 1.5 Show that the series (a – 6)(a – 26) „3 + (a- b)(a- 26)(a- 35) | z+- 2! 3! 4! converges…

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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…

Q: Check the convergence of the following series: k=1 ak²+bk+c dk² + ek + f where a, b, c, d, e, and f…

A: The given series is a rational function of k, and it is an infinite series as it goes from k=1 to ∞.…

Q: We will prove the Cauchy-Schwarz inequality for infinite series. Let (a,) and (bm) be two sequences…

A: Since you have asked multiple subparts question, we will solve the first three subparts of the…