Use |S – SN|

Q: What are all of the values of x ,such that E-1)n+1(n)* converges? x1.2 O x<1.30 x<0,40

A: By lebnitz test we observe n^x tends to inf gives zero only when x&lt;0.

Q: n n converges, because 0 < < 1 and an 2n + 1 2n + 1 ni an is decreasing. 2n + 1 True False

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Q: 4n – 9 5n + 4 S - Given that sequence {an} = { (а) Show that the sequence is monotonically…

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Q: 3. Assume the sequence of positive numbers (sn) increases monotonically to infinity. Prove that Sn+1…

A: Let Sn be a sequence of positive numbers sn increase monotonically to infinity. ⇒limn→∞sn=∞     ∵ sn…

Q: The series 2 ÷, n =0 x" |x| >1 has a sum equal to: Select one: а. х b. х— 1 C. 1 1-x d. 1 х —1

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Q: given parameters a,b > o and the given sequence x₁= b X = n+1 4 (x₂ + 4a) n Xn a. Show that a b.…

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Q: 23.Determine the an so that the equation ∞∑n=1nanxn−1+2∞∑n=0anxn=0∑n=1∞nanxn−1+2∑n=0∞anxn=0 is…

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Q: 8 Let k(x) = |x|", n = 1,2, ... Is k differentiable for all x and every n? Find a formula for k' (x)…

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Q: 4n The sequence an %3D 12 + 64n2 O A None of these O B. diverges 1 Oc. Converges to 16 1 O D.…

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Q: 8. {(G 3n | The sequence 1+3n n=1 Diverges 1 Converges to O None Converges to Ve OConverges to e

A: we have to solve

Q: Find the exact value of n! and then approximate n! using Stirling’s Formula.    n = 12

A: Exact value: Since n!=n(n-1)(n-2)....3.2.1 Given that n=12 So…

Q: (a) Show that Sn/√n has mean 0 and standard deviation 1. (b) Using the Central Limit Theorem, show…

A: Given that the position of the walk after n steps is Sn=S0+∑i=1nXi  where S0=0 and Xi are…

Q: nxn 5) Find all values of x for which Σn=1 (n+1)(2x+1)″ converges absolutely.

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Q: Use the difference a+1 - an to show that the given sequence {an} is strictly increasing or strictly…

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Q: 1 diverges by comparing with n-. 16. Show that n² – 3 n=2 n=2

A: Given: The series ∑n=2∞1n2-3 To show: The given series converges by comparing with ∑n=2∞n-1.

Q: Use |S – SN| < bN+1 to find the smallest value of N such that SN approximates the value of the sum S…

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Q: How and why does the first summation in this picture turn into the finall summation?

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Q: The minimum value of N such that the remainder estimate given in the text guarantees that SN…

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Q: che limit to the following sequence. Round your answer to the nearest hundredth. =[ 10n2 +3n+1 ]/…

A: We will find the limit of the sequence.

Q: Use |S – SN| < bN +1 to find the smallest value of N such that Sy approximates the value of the sum…

A: According to the given information, it is required to find the smallest value of N such that SN…

Q: The interval [0,5] is partitioned into nn equal subintervals, and a number xi is arbitrarily chosen…

A: The given interval is [0,5]. Find the xi.

Q: If |x| < 1, then, for any real number r, the series E(-1)* (2)x²* k=0 converges to (1 + x²)". Select…

A: Given series is ∑k=0∞−1krkx2k We have to check whether the statement, "if x&lt;1, then, for any real…

Q: 2n + 5n 11. Use the integral test to show that n=1 converges. n"

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Q: Q3. A sequence of integers o, ₁, is defined by xo = 2,₁ = 5 and m = xm-1 + 2xm-2 for m≥ 2. Prove…

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Q: Find the smallest number n of terms needed to 9 obtain an approximation of the series k10 k=1…

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Q: (A) True B) False The sequence {x}to, where xn = Sn² 20" is convergent. n! :

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Q: A sequence Sn is siad to be bounded below if there is some number N such that .... .a .b Sn+ n +1 .C…

A: Consider the given information. Now, define bounded. A sequence an is said to be bounded if and only…

Q: For which an does the sequence {an}-1 converge? Select all that apply. OA. sin(3n) an n2 OB. Зп — 1…

A: We will answer the first three parts for you. Kindly repost the question specifying the desired…

Q: Q\ Is the sequence (Vn + 11 – vn+1)y bounded ? nEN Neither Yes No

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Q: Use the difference an+1 - an to show that the given sequence {an} is strictly increasing or strictly…

A: given sequence n7n-6n=1∞

Q: b) An engineer seeks to establish an empirical link between the temperature of a component and its…

A: Given data Temperature is independent variable and Resistance is the dependent variable

Q: Which of the following sequence is divergent? 3- 2n²\ n² + 1 S ( 3 sinh n sin n °{2(#)} 0{-3.} None…

A: Sol:- Check for Sequence Divergent Option :- First ∑n=0∞ 3-2n2n2+1Apply Series Divergence TestIf…

Q: There are 25 prime numbers less than 100. The Prime Number Theorem states that the number of primes…

A: Given, Px≈x/lnx     ......(1) (a) find P(1000) put x=1000 in equation 1…

Q: Q2/ Let x(n) be a 4-point sequence. Compute the DFT of x(n). 1 x (n) =- 0<n<3 0otherwise ans. X(k)…

A: …

Q: Q1:Proof the following Limits : C. Ln=1n! e-n

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Q: Use the difference an+1 – An to show that the sequence {n – 7"t00 is strictly increasing or strictly…

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Q: 100 4. If En=1 an converges absolutely, then n=1 an converges conditionally (C). 1 For p > 1, the…

A: Theorem : If the series ∑n=1∞|an| converges, then the series ∑n=1∞an also converges.…

Q: 6n The sequence dn V10 + 25n? 6 O A. Converges to 25 3 O B. Converges to 3 OC. diverges 6 O D.…

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Q: What test would you use to test the convergenc 2n+1 n=1 n³-4n²+6 2. ΣΤ-1 (-1)"+1 (n²+3)² 3. Σ-1 5sec…

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Q: A 2-person barber shop has 5 chairs to accommodate waiting customers. Poten- tial customers, who…

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Q: Give the limit of the following sequences. nV14 - 3n? +* 7n + 2n An 3n – 4 2nn B = sin 3 n* + 2nv2…

A: As per our guidelines, we are supposed to solve only first three subparts. Kindly repost other…

Q: the interval of convergence. (x+7)" ( a) Σ In n=1 x" (b) En! n"

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Q: Find all the values of x suc * 11" (x")(n +1) (n + 4) n=1 The series is convergent from x = le

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Q: Given the expression an = V4n² + 3n – 2n for n > 1 Check whether this is convergent or divergent: an…

A: The given sequence is a an=Sqrt(4n2+3n) -2n.

Q: The first four terms of the sequence (Xn) are given by X1= 1, X2 = 5, X3 = 21, X4= 85. Therefore,…

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Q: Given the expression an = V4n² + 3n – 2n for n >1 Check whether this is convergent or divergent:…

A: solution:-an=4n2+3n-2n   for   n≥1Divergent…

Q: Use the Integral Test to determine the converge 2 ke - 6k? k = 1 Select the correct choice below…

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Q: (-1)"n2 + n The sequence {bn}, where bn converges. 4n2+1 O True O False

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Q: write down detailed e− N-proofs  i) (√n+7)/(n+5) converges.  ii) (n2−3i)/(2n3+2i) converges

A: Follow the steps.

Q: 5. At a local university, English instructors are supposed to grade essays in a class so thất the…

A: Given that n=22