(a) Find the least positive k E N such that 3* =10 1. (b) Using this k, prove: for all m e N, 3m =10 3m%k

Q: 1. Try to use the ratio test or the root test to determine if the following converge or diverge. If…

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Q: For what value of x is the infinite series D! x n-0 n diverges? OA. X= e O B. None of these. OC.Xe

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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: Find the radius of convergence for: n°x" 3n n=D1

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Q: et For which values of p does converge? (1 +e2*)P

A: Given:∑n=1∞ex1+e2xp

Q: 1. u',= E(X")= the co-efficient of i" o" in the expansion of ø (@) in series n! of ascending powers…

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Q: Equating the coefficients of t" in the following series: æ(1+ 2n) Pn t" – (1+ n)Pn t"+1 – nPn t"-1]…

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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: For what values of x does the series ∞∑n=0xn / n+1 converge?

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Q: Let y be a function of x & z is a real constant. Find the series solution of (x²-z) y"+9xy'+12 y=1…

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Q: Find the values of x for which the series converges. E(-3)"x" n = 1

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Q: Find the interval of convergence for Σ (k + 2) æ(k+2) k + 3 а) O1-2, 2) b) О (-1,1) с) O1-1, 1) d) O…

A: Put k+2 = t  We get  ∑(t xt )/(t+1)

Q: Find the function represented by the power series. 00 X+5 10 n= 0 10 O A. X-5 10 O B. x² - 5 10 C.…

A: Proceed as shown below

Q: For what values of z does the series n²(¹3)" =1 converge? Find the sum.

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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: 4. The Talor series for e* at the point x = 0 is given by x? x3 x* + 3! e* = 1+x + 4! 5! How many…

A: Using (n+1) terms of the Taylor series gives an error bound of Rn(x+h)=hn+1(n+1)!fn+1(c) For x=0,…

Q: What function is represented by the power series E=o(-1)"x3n? n3D0 a. 1-x3 b. 1+x3 с. e-3x d. e3x…

A: The solution is given as

Q: 3) Does E-1 ati converge? 00

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Q: For which (positive real) s does the series co nv er g

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Q: V2+cos (n2+1) Use the basic comparison test to determine whether E1 n=D1 converges or n+en diverges.

A: To check the Convergency of the given series. We apply here Simple comparison Test and Ratio Test of…

Q: Find all the values of x such that the given series would converge. (- 1)"8"x" (9 + u^) 8. n=1

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Q: The Taylor series for f(x) = sin(x) at c = 1/4 is Cx (x – 1/4)*. k= Find the first few coefficients.…

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Q: b) Suppose (xn) does not converge to 0. Then there exists e > 0 such that all except for finitely…

A: Let us suppose the following sequence xn=1,0,1,0,1,0,..... We have to see that the odd terms are 1…

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

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Q: 1.2 Determine whether or not the series of functions {Sn(x)} = {>*-1} converges uniformly k=1 on…

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Q: H.W Given a sequence x(n) for 0sns3, where x(0) = 1, x(1) = 1, x(2) = -1, and x(3) 0, compute its…

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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: Find all the values of x such that the given series would converge. (– 1)*11"x" n=1 (vn + 10)

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Q: For what values of x does the series converge conditionally? Σ (-1)^(4x+7)" n=0 OA. x = -2 3 OB. X=…

A: This is a problem related to series and sum calculation. Based on the general formula we will answer…

Q: 3) For which a does converge? Justify your answer. n(ln n)ª n=2

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

Q: 2) For which value alpa does the Gauss-seidel method converge? A = 9.

A: Since you have asked multiple question, we will solve the second question for you. If you want any…

Q: For which values of p does En=1 00 en (1+e9n)4p converge?

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Q: Σ 4(k!) ² (2k)*! K=( a. Converges completely because re? b. diverges because r=? C. ratio test is…

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Q: 1. Determine whether the following converge or not (a) E k3 +1 k=1 2+1 (b) k=1

A: The given sequence is                                     ∑k=1∞k3k3+1  Consider     ak=k3k3+1 Now…

Q: 2. (a) For n ≥ 0 and x E R, prove that (b) Prove n n Σ ^ (^.) 2^* (1 - 2)"-* k k=0 = = In. n x)n-k…

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Q: 1 Use appropriate tests to determine if E(-1)"+1, converges. n* log(n) + n! n=1

A: use appropriate test to determine whether the series ∑n=1∞-1n+11n4logn+n! converges according to…

Q: 18 For which of the following series does the ratio test fail? 00 00 k (b) 3k 00 (e) None Σ (a) (c)…

A: The (a) option is correct.in this option the ratio test fails.

Q: The sequence {G 3n+2 n=1 O None converges to e O diverges converges to Ve? converges to e3

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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: 5. Determine the range of K for stability of the following characteristic equation, (b) s3 + (K +…

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Q: Find the exact value of n! and then approximate n! using Stirling’s Formula.   n = 15

A: Given n=15

Q: For what values of x does the series E(Vn +1- Vn)(x – 3)" n=1 a) absolutely? b) conditionally?

A: Here, an = (√(n+1)-√n). Now,

Q: For what values of x does the series E-1 n=1 x21+3 12² converge?

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Q: For which values of p does E=1 (1+eon)4p converge?

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Q: E x" by itself to construct a series fo E 00 Multiply the series %3D (1 – x)(1 – x)'

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Q: If |Xn+2 − Xn+1| < |¤n+1 − xn| for all n E N then (xn) converges. -

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Q: Show E-2 1/nº 1.

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Q: Evaluate E-2(1/(k² – 1)) by finding the limits as n→o of the series' nth partial sum.

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Q: The function f(x) = 9x ln(1+ x) is represented as a power series %3D 00 Cna". n=0

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