Apply the power series method. Show the details. y" + y = 0

Q: Determine if the series converges or diverges. If it converges, find its sum. Fully justify your…

A: Performing ratio test to check for convergence.

Q: State where the power series is centered. (-1)"(2n – 1) „n Σ * 2"n! n = 1

A: Solving

Q: Suastion 2 8, と what is the power Series expor sion と 1. -()け a)3 と 3 と-○ c)を

A:

Q: s: find the sum of the series or show that it diverges

A:

Q: State where the power series is centered. Ï (-1)^(x – 57)6n (-1)"(х - 5л)бл n = 0 (6n)!

A: Center is 5π .

Q: n+ Vn n=1

A:

Q: In the givn equation as folows ,  state where the power series is centered:-

A: Given: ∑n=1∞-1n2n-12nn!xn Concept Used: Consider a power series ∑n=1∞anx-an Here 'a' is the center…

Q: 4" 2.

A:

Q: State where the power series is centered. Σ n = 0

A: We have to find center of power series

Q: What is a power series? What is the difference between a series of constants and a power series?

A: Query- What is a power series? What is the difference between a series of constants and a power…

Q: Determine whether the series converges or diverges, if it converges give the value.

A: Given∑n=2∞ne-n ...(1)e-n=1enNow substitute this value in equation (1) we get that∑n=2∞nenNow we…

Q: Determine whether the series converges or diverges. sin?(n) 4 n = 1 n* + 2 O converges O diverges

A:

Q: Does the series converge or diverge?

A:

Q: fine the term DeComposite Series?

A: Not sure what does "fine the term ..." mean. I have assumed you intended to write "Define the…

Q: a) ΣΣ п n=0

A:

Q: Is the series convergent or divergent? Justify the answer

A: Follow the procedure given below.

Q: Write out the first five terms for the series: (-1)** 2n Does this series converge or diverge?…

A: Consider the given alternative series as ∑n=1∞-1n+12n. Answer: The given series is converge It is…

Q: Σ Vn5 + 7 n%3=

A: We have to find cheek converges

Q: can you please answer both questions. Decide whether those two series will converge. Thank you

A: Given series

Q: Σ n? sin n n=1

A:

Q: State where the power series is centered. Σ 5 (-1)^(x – 57)3n (3n)! n= 0

A: To find the center of power series, set the expression containing 'x'(inside parenthesis) equal to…

Q: Define error of series with formula?

A: Define error of series with formula?

Q: Construct the exponentially smoothed series using a speed of decline 0.2

A: From the given information, the value of α is 0.2. The formula for Exponential smoothing is,…

Q: use the binomial series to estimate Y10, Calculate the first three terms.

A: According to binomial theorem 1+xn=1+nx+nn-12!x2+nn-1n-23!x3+... Now…

Q: power series (n + 1)! n=0

A:

Q: n2 n=1 Using the alternating series error test, what is the least number of terms necessary to…

A: Given-              ∑n=1∞-1n+1n2 we have to find the least number to approximate the series.

Q: Evaluate the series or state that it diverges.

A: Given: S=∑k=0∞120.2k+320.8k for finding given summation, first we expand given expression so,…

Q: State where the power series is centered. 00 (-1)"(x – 5x)8n Σ n = 0 (8n)!

A:

Q: State where the power series is centered. Ση n = 0 1

A: We are going to find

Q: LX Solve the dlifferontial equation using the power series methbd.

A:

Q: (1))3" 2.

A: The given series is : ∑n=0∞-1n3n2n    Applying  Ratio test to the above series.…

Q: etermine if the following series converges or diverges?

A: Apply ratio test

Q: 5n2 n=17n³ – 2n

A:

Q: Find the positive values of p for which the series coverages

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Q: State where the power series is centered. Σ (−1)"(x – 7π)5η (5η)! n = 0

A:

Q: State where the power series is centered. Σ Š (-1)"(x – 6x) 5n | n = 0 (5n)!

A: We use definition of centered of power series.

Q: a. x K=I 34 K!

A: We can solve this as follows:

Q: 3" Σ A=1

A: WE USE THE COMPARISION TEST

Q: Does the series converge or diverge? Explain.

A:

Q: 3. n²+3n

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Q: Use the power series to solve : y" - x y'-2 y =4x %3D

A: We have to solve the given differential equation by Power series .

Q: Use the test of comparison to determine whether the series converges

A: Given summation is∑n=1∞3n+2n12n+9n

Q: Does the series diverges or converges?. Give reason for your answer. * .Then find the formula for…

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Q: State where the power series is centered. ř (-1)"(x - 3)6n (6n)! n= 0

A:

Q: Does the series converge, if so, where?

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Q: State where the power series is centered. Σπ.χ. - Ο

A:

Q: Consider the series ++++ + .. .... Does the series converge or diverge?

A:

Q: State where the power series is centered. Σ nx" n= 0

A: A power series centred at (or about) x=c is a series of terms such that all terms are non-negative…

Q: State where the power series is centered. Σ (-1)"(x – 6x)ªn (4n)! n - 0

A:

Q: Use power series to solve y-y = 0 -y3=

A: Given that y'-y=0 To solve by using power series.