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

Q: n = 0

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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.

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Q: Express the function as the sum of a power series by first using partial fractions. (Give your power…

A: As per our company's guidelines we are supposed to answer first question only. Kindly repost the…

Q: Find the sum of the convergent series by using a well-known function. Identify the function and…

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Q: Find the sum of the convergent series. (Round your answer to four decimal places.) Σ (sin(3))" n = 1…

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Q: What happens if you add a finite number of terms to a convergent series?

A: The convergent series takes a finite value or we can say that convergent series give a finite sum.

Q: use the Power Series Method to solve for the general solution. express your final answer in sigma…

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Q: it is always that when the series equal to zero it converges and when it is nonzero it diverges ?

A: For a series to be convergent we must have limn→∞an=0. But the converse is not true.  For example:…

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: How many terms of the convergent series should be used to estimate its value with error at most…

A: Given series ∑n=1∞7n1.1.

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

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Q: Write the first five terms (or the series in summation notation) of the power series for x2…

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Q: Solve y’’- y = 0 with a series solution. How does uniqueness play an important role?

A: we have y"-y=0 --(1)Let y= ∑n=0∞ anxn --(2)Differentiating (2) with respect to x we gety'=∑n=1∞…

Q: (-1)r+1. n=1 と(-1)"+1 n2 2]

A: Topic:- sequence and series

Q: Find a series solution for у" -ху %3D 0 around the point xo = -2

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Q: Comparison Test

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Q: The first term of binomial series is -8 40 $$x$$

A: The first term of binomial series depends on the given function. First we need a function for which…

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

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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: Find the sum of the series correct to three decimal places.

A: solve the series

Q: Is this series convergent or divergent?

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

Q: 42n (x + 4)" is 8n n=0 The given power series : convergent if |(x + 4)| < ( Write your answer up to…

A: Given, the power series ∑n=0∞42n8nx+4n is convergent. Then we have to find x+4&lt;?.

Q: Using Taylor Series, what is the value of yo(4) if y'=x+y² for y(0)=1?

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

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Q: Find the sum of the convergent series. 00 4 п(п + 2) n=1

A: Given series,

Q: find a power series representation for this function?

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Q: 1-x хр ха ес

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Q: 1 f (x) = %3D 1-V2x

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Q: Σ 42n - (x + 3)" is convergent if The given power series : 9n n=0 |(x+ 3)| < ( Write your answer up…

A: using the fact that power series is convergent whenever |x-a|&lt;R;  R is radius of convergence

Q: In the given equation as folows , write a power series that has the indicated interval of…

A: Given :                  The interval (-3,3) Calculation :                      Take the power…

Q: Define error of series with formula?

A: Define error of series with formula?

Q: Find the sum of the convergent series by using a well-known function. Identify the function and…

A: Given series is ∑n=0∞-1n12n+1......(1) We have a well known function  ∑n=0∞-1nx2n+12n+1=tan-1x,…

Q: Find the sum of the series if it converges. Hint: Rationalize

A: Rationalizing the given series: n+1-n(n+1+n)(n+1-n)=n+1-nn+1-n= n+1-n

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: Find the sum of the infinue series: En-2 n log [(1+²) ² (1+n)] (logn") (log(n+1)(n+1)) is

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Q: How to expand a sine function into power series? Please help me to understand.

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Q: How can you sometimes use power series to estimate the values of nonelementary definite integrals?…

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Q: How can you proof that this series is Converges?

A: We have a series ∑x=1∞cx2 We can use the integral test for convergence. It says that ∑x=1∞ax…

Q: It's not super specific, but I'm curious if I could get help on explaining how to represent a…

A: Let us assume a geometric power series, i.e., ∑n=0∞arn=ar0+ar1+ar2+............+∞ Where a is the…

Q: Solve using Power Series Centred Around Zero. Xy" + (1-x) y' + 2y=0 2=REZ+

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Q: Express F in terms of functions that you know the power series expansion for

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Q: Solve y' = yx² by using power series without recurrence method. %3D

A: y′ =yx2 First-order separable Ordinary Differential Equation A first-order separable ODE should…

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

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

Q: What does it mean for infinite series to diverge?

A: Given: Infinite series to diverge:

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

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