4. Determine the value of n such that Sn can be used to approximate the number of the following series with an error of not more than 0.005! 00 3 (-1)*+1 (,) 2.n!) n=1

Q: 13. Verify that the alternating series test applies to the series S (-1)" (-1)" (n² + 2)10 Then use…

A: We need to first verify whether the alternating series test applies to the given series.…

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: 4. Find the sum of the following series: n=1 1 (a+n)(a+n+ 1)(a +n + 2) (a-n, n = N).

A: Introduction: The sequence of partial sums is very significant in determining the sum of an infinite…

Q: Find the sum of the following series: {1-0.09 +0.092 -0.09³ +... -0.0925} a. Find a, r, and n. n b.…

A: The given series is 1-0.09+0.092-0.093+...-0.0925   When the ratio of consecitive terms of a series…

Q: 6. Are the following series convergent? Why? (a). (b) 00 n=1 α 2 (3n-1)1.3 n=1 n2 – 1 2η2 + η

A: The given series are ,  (a).        ∑n=1∞2(3n-1)1.3 (b).         ∑n=1∞ n2-12n2+n (.)  Necessary…

Q: 5.) Determine the convergence or divergence of the series In n=1

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Q: `6. Evaluate the following geometric series as exact numbers. If the series diverges, then state…

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Q: 10. Determine whether the given series converges or diverges. If it converges, find its sum. -2 n=0…

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Q: How many terms of the series (-1)"–1 do we need to add in order to find the sum to the accuracy…

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Q: 3. Find the exact value of the series S = > n(n +2)* n=1

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Q: 4. Does the following series 1 converge? Explain. n¹4 n!

A: The given series is  ∑n=1∞ n4 4nn!                Let  an = n4 4nn!  then  an+1 = n+14…

Q: 5. This question has two (related) parts. (a) Show that the series test(s) discussed in class. n=1…

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Q: Where does the subsequence series Nk = 2kpi come from? While I know it's used to specify the set of…

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Q: 4 3. Let S = E(-1)n+11 and let S4 = E(-1)n+11. Then S4 < S since the next term in the series is…

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Q: Estimate 16 dr using the 4th partial sum of a power series. How accurate is this estimate?

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Q: Approximate the sum of the series to four decimal places. (-1)^-1 7 (2n-1)! Select the correct…

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Q: 32. Show if the series converges or diverges using the Alternating Series test 00 1n+1 Vn n=1

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Q: 3. Determine the sum of the following series, Σ n=0 Π (n + 1)!

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Q: (3n)! 3 (n!)³ n=1

A: We can test the convergence and find the interval and radius of convergence.

Q: 4.- Suppose we have a number with infinite decimals of the form 0.d₁d₂d3d4... (where each d₂ = 0, 2,…

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Q: Find the sum of the convergent series. 1+1/1/2+. 4+2 +1+

A: Given series 4+2+1+12+.....

Q: S = -1)n+1 8n n=1

A: Alternating series test: Suppose we have a series ∑an with an=(-1)n+1bn where bn≥0 and limn→∞ bn = 0…

Q: 1. a. List out the first four terms of the following series: > n(n – 1)a,nx"-2 = In%=2 b. Combine…

A: Solution of the problem as follows

Q: 6. What is the sum of the series 元 17 + πT TE (A) (B) (C) e+π e + 1 e اسه TU TT ++ (-1) +1/+ +... ?…

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Q: Q2-)Determine the sum of the following series: 4 1- 2n=1 (4n-3)(4n+1). 2- 2n=0

A: 1. We use partial fractions to find the sum of the given series. 2. We use the sum of geometric…

Q: Consider the series (-1)n*(3n2+n+5)/(4n3+2) = 5/2 - 3/2 + 19/32 - 7/22

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Q: b. C. a. d. Use the AST to show this series converges. Approximate the sum by calculating $₁. Find a…

A: An alternating series is given.

Q: 11. Series k=1 For each of the following sequences {a}, decide wether the series Σak is convergent…

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