Please solve X"+tX=O in power series and state the kind of ODE it is. Thanks

Q: Find if the series converges or diverges and explain what test used and show steps, help is needed,…

A: we will test the convergent by ratio test

Q: please explain with clear steps why is it important to center the  power series at the same x value…

A: We will explain here with clear steps why is it important to center the power series at the same x…

Q: Find the sum of the geometric series if it converges; otherwise indicate it diverges.

A:

Q: Explain how to use a geometric power series to represent a function of the form f(x) = %3D

A: As no particular range is mentioned, the series is expanded about origin. This function can be…

Q: what is the 20th term in a geometric series whose 5th term is 48 and 12th term is 6144? Please show…

A: In a geometric series nth term an=arn-1  where a = first term             r = common ratio  Given…

Q: Solve by power series 1- (x+1)y' – (x + 2)y = 0

A:

Q: Please solve X''+tX=0 in power series and state the kind of ODE it is. Thanks

A: We will find out the required solution.

Q: Please solve X"+tX=0 in power series and state the kind of ODE it is. Thanks

A: The given problem is to solve the given differential equation in the method of power series. Given…

Q: 2. ク

A: Convergence of the seriese

Q: cos (n) 4) Is an alternating series? Does it converge ? Does it converge absolutely? Explain…

A:

Q: Please show all the steps, thank you! Determine if the following series converge or diverge:

A: Solution of the problem as follows

Q: Evaluate the indefinite integrals as an infinite series and give answer in summation notation. Also…

A: Here we will find out required integral.

Q: Use power series to solve y' = 2y, y(0) = 5. %3D

A:

Q: How can an elementary function be represented as a power series?

A: An elementary function can be represented by using Taylor series expansions. We use successive…

Q: If the ratio of the geometric series Ir|<1, then it is converge and it's sum is:

A:

Q: I - 3 9(x): 1² – 6x + 10

A: Mentioned below is the answer

Q: As a general rule, is it advisable to difference a  time-series more than 1–2 times? Why or why not?

A: The objective is specify whether it is advisable to  difference a  time-series more than 1–2 times.

Q: Comparison Test

A:

Q: _xy" + 2y' — xy = sech²(x)

A: Given: xy''+2y'−xy=sech2(y) To find: Power series

Q: Find the exact sum of the series if pessible; If not, estimate with S4 and State

A:

Q: Find the first term of the series whose second and subsequent terms are, 8, 3, 0,-1, 0, ...

A: Given, the series whose second and subsequent terms are                         8, 3, 0, -1, 0, . .…

Q: The sum to infinity of a geometric series is five times the first term. Find the common ratio. r=

A:

Q: Evaluate the indefinite integral as an infinite series and give answer in summation notation. Also…

A:

Q: • Decide Calculate the sum. if this real series is Fonyergent or not Ornot. 9s well.

A:

Q: Is this series convergent or divergent?

A: This question can be solved using the concept of root test.

Q: Use substitution of power series to approximate cosh (2x) dx

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Q: (х + 1) %D

A: According to the given information, it is required to determine the two power series solution about…

Q: Find all the values of x such that the given series would converge. n! n=1 IM:

A:

Q: In your own words, describe how a function defined by a power series behaves like a polynomial.

A: Power series of the form ∑n=1∞anxn and a polynomial is of the form ∑n=1kanxn

Q: 1-x хр ха ес

A:

Q: find the solution of the expression y(x) with the power Series in x=0?

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Q: Give an example of a convergent infinite series whose sum equals 2/11 . Explain how you know that…

A: To find the series which is convergent and whose sum is 211

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

A: Given series

Q: Define error of series with formula?

A: Define error of series with formula?

Q: The sum of the first three terms of a geometric series, whose first term is 2 and whose common ratio…

A: We have to apply the formula of Sn(sum of n term of geometric series)

Q: Differentiate or integrate number 96 to find the power series for the function

A: We have to find power series

Q: How do I solve this equation? I am not given a specific test to use, i am supposed to pick one…

A:

Q: By assuming solution as a series form

A: The given second order differential equation is x2d2y(x)dx2+xdy(x)dx+x2y(x)=0 Suppose a series…

Q: With explanation, find a power series that converges to:

A:

Q: Decide whether this series converges or not and if it converges find it. Σ 3 5n

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Q: The power series in the image converges to cos x for ALL values of x. Using this fact and…

A: The derivative of the function cos(x) is -sin(x). We use this fact to find the power series that…

Q: n series converges. Use interval notation with exact values. 10,10)

A:

Q: Describe two ways to show that the geometric series ∑ , converges when ∣r∣ &lt; 1. Verify that both…

A: Consider the given series ∑n=0∞arn.

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

A:

Q: Find the sum of the series (-1)"-1 (п + 1)пi"-1 n=1

A: We find the sum of the series by the sum of the known series.  We know that (1+x) -1 =…

Q: Solve using Power Series Centred Around Zero. xy" + 2y' — xy = sech²(y)

A: Given: xy''+2y'-xy=sech2(y) To find: Power series

Q: Please state whether the series converges or diverges

A: We will check whether the given series is convergent or divergent.

Q: The value of limx→o ex-1-x x² by using series is

A: I have given the answer in the next step. Hope you understand that

Q: Illustrate Power Series 1/(1-x) ?

A: Given, 11-x

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

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