Consider the following power series. Let ak = Σ(-1)*(x-6)* k=1 R = 8 (-1)k 8k (x-6)k. Find the following limit. ak 1 lim k→∞ 7. |³k + ¹ |-|(x-6)* ak = X Find the interval I and radius of convergence R for the given power series. (Enter your answer for interval of convergence using interval notation. I= (-6,14). X

Q: Q3. For the following power series: En=125 (4x – 16)" i. Find the radius of convergence, ii.…

A: Given power series is ,

Q: 2. ( 16 p.) a) Calculate the interval of convergence of the following series. (-1)"+1(х — 3)" n+1…

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Q: 2. I) Find the centre, radius, and interval of convergence for the given power series. 1 Σ (13) n…

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Q: Q2. (a) Find the following series interval of convergence and, within this interval, the sum of the…

A: Answer is mentioned below

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A: To find the convergence range of the given series

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A: Given seriesg(x)=∑n=0∞(4x−2)n4nn+2Which can be written…

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A: Note: As per our guidelines, we can solve first question. Please repost the remaining questions.

Q: #8: If the sum s of the series 3(-1)" (n+2) n=0 is approximated by 3(-1)" Sm (n+2) find the smallest…

A: The smallest possible m will be , m = 2.

Q: 3. Find the interval of convergence of the series ☎ n=1 (-1)"+¹(x-2)" 3"-n

A: Find the interval of convergence of the series

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Q: (b) (a) -5 Q7) L(y") = a) s²L(y(x)) + sy(0) - y'(0) c) s²L(y(x))-sy(0) - y'(0) b) s² L(y(x)) + sy(0)…

A: We have to find the correct choice.

Q: Find the radius and interval of convergence for the following series: (x - 2)" 10" a. 8 n=0 Radius=…

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Q: 3. ( for ) Find the power series representation f(x) = Σen(x - a)" n=0 f(x) = = 1 about x=a=0. Also…

A: We have to find the power series representation fx=x1+x5 about x=0.

Q: Suppose that the series (a) (an+b)xn n=1 (b) Σan(x-7)n n=1 (c) bn(x-2)4n n=1 n=1 anx has radius of…

A: Given , Series  ∑n=1∞anxn has radius of convergence  '5' and series  ∑n=1∞bnxn has radius of…

Q: a) Find the length of the curve y = 5x/T - 6, 1<r< 3.

A: Arc length of the curve along x-axis

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Q: For the following function, find the full power series centered at x = 0 and then give the first 5…

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Q: Analyse the convergence of the sequence {fn} where fu(x) = on R. 1+ na²

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Q: Q3: Find the interval of convergence of the following series Inx" Σ Vn +3 3" IM IM

A: Here we find interval of convergence of given series

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Q: (b) Determine the convergence of the series a, for the following cases: 4r2-3r +2 2r4 +r2 +10' 3r+5…

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Q: Find the radii of convergence for each of the following power series. (a) n=1 n(x - 1)" 2n

A: Since you have posted a multiple question according to guildlines I will solve first question for…