Suppose we are given a power series centered at 0 Σ anx". n=0 Come up with a power series (not necessarily centered at 0) that converges only at x = diverges elsewhere, and the sum of the seires at x = 153 is 153. Use computations to back up your 153 but answer.

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A: We will find the series is converge or diverge using the integral test.Below find the solution in…

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A: We have to solve given problem:

Q: In  the given question as attached here verify that the Ratio Test is inconclusive for the p-series.…

A: Verify that the Ratio Test is inconclusive for the p-series.                   ∑n=1∞1n4

Q: Suppose we are given a power series centered at 0 Σ anx". n=0

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Q: Suppose that (a) n=0 Cnxn converges when x = -4 and diverges when x = 6. What can be said about the…

A: As per company guidelines we are allowed to solve maximum three sub-parts so i am solving first…

Q: Compute the value of the improper integral. (If the integral diverges to oo, type oo; if the…

A: Here we integrate the following integral

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Q: The divergence test applied to the series 4k (7k + 9)* tells us that the series converges.

A: Given: Here,              ak=4k(7k+9)3≈4k73k3=473k2=bk(say) Now,                 limk→∞ akbk=limk→∞…

Q: In  the given question as folows , find the interval of convergence of the power series. (Be sure to…

A: Consider the series : ∑n=0∞2xn Find the interval of convergence. The series ∑n=0∞arn is a geometric…

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Q: Help with 1 and 4 please

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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A: Given: f(x)=x Power series represents Taylor and Maclaurin series. General form of a power series…

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Q: In the given equation as follows, confirm that the Integral Test can be applied to the series. Then…

A: ∑n=1∞ 23n+5Apply the constant multiplication rule:  ∑c·an=c·∑an=2·∑n=1∞ 13n+5   Let N be a natural…

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A: Given : ∑n=1∞n2n+3

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A: recall:Radius of convergence of power seriesA series of the form ∑n=0∞ anz-z0n,where an∈c and z0∈c…

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A: Given: The expression 11+x2, To find: The power series representation and the interval of…

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A: Given series is  ∑n=0∞xkn=∑n=0∞xnkn where an=1kn.

Q: The series C,(x +3)" converges at æ = 2 and diverges at æ = -12. Based on this information, what can…

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Q: Compare with an improper integral to determine whether the series converges ΣΤΕΥ n(In(n))e

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Q: Find the positive values of p for which the series converges. (Enter your answer using interval…

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Q: Express the series in terms of elementary functions and find the where the series converges (1+ a*)…

A: We have,

Q: Compare with an improper integral to determine whether the series converges

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Q: the sum of the two parts of the Noni series Sn ar

A: Given : It represent Geometric series :

Q: Use the ratio test to determine whether the series converges or diverges. If the test is…

A: This question is based on ratio test.

Q: Is the series n(sin^2(n))/(1+n^3) convergent or divergent for n=1 to infinity?

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Q: 7. f(x) = 유 1+x

A: Hi, since you have asked multiple questions, we will solve the first question for you. If want any…

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Q: Compute the value of the improper integral. (If the integral diverges to oo, type o0; if the…

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Q: Verify that the series Σ n=1 satisfies the conditions of the Integral Test, then use the Integral…

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Q: Suppose that the series a,(x – 1)" converges for r = 3 and diverges for x = -4. (a) Does this power…

A: Given that ∑n=0∞an(x-1)n  The series converges for x=3. The series diverges for x=-4. (a) At x=0,…

Q: 3. Suppose that the following alternating series converges. (-1)" n2" Determine the number values…

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Q: If L=3z-i of a power series, what is the radius of convergence i 3 1 3i 1

A: Given for a complex power series is the limit L=3|z-i|.

Q: Find the sum of the series for the values of x, for when the series converges.

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Q: State what it means for a series to be absolutely convergent. As well, if >Ja, converg * (2n +1) 1..…

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Q: Subtract the infinite series of ln(1 – x) from In(1 + x) to get a power series for: + x Σ In %3D n=1…

A: Given:

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Q: What are the values of x that make the next series convergent (sin(x))" n n=1

A: To find the values of x for which the fpllowing series converges…

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Q: Suppose that Cnxn converges when x = -4 and diverges when x = 6. What can be said about the…

A: The posted question has multi parts. But according to guidelines we will solve the first three…

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A: The expansion for ln1+x can be written as follows:

Q: Compute the value of the following improper integral if it converges. If it diverges, enter INF if…

A: Given:

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A: Consider the function fx=sinhx2. Rewrite the given function using sinh(x)=ex-e-x2.

Q: Suppose we are given a power series centered at 0 Σ anx". n=0

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