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

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: What is the fundamental difference between power series and other types of series (like harmonic,…

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Q: this series? How do you use the tests' conditions to figure

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Q: Showing your steps, determine whether the series converges or diverges using the Comparison Test. Σ…

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Q: Which series converge, and which diverge? Give reasons for your answers. If a series converges, find…

A: First, we expand the summation

Q: Identify which type of infinite series the given series belongs to. Then, use it determine whether…

A: To find the nature of this series, we have to simplify the term given.

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

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Q: 1+sin (n) 2. Determine whether the series is convergent explain why. Ln=1

A: We have to test the series

Q: SA We have seen that the harmonic series is a divergent series whose terms approach 0. Show that 8,…

A: Given :∑n=1∞ In1+1nClaim :To show that the series is diverges with limn→∞an=0.

Q: This is nothing specific, but I was wondering if I could get an example provided as to how to…

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Q: 3. Evaluate the indefinite integral as a power series. *x – tan¬1 x dx x2

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Q: Find the sum of the given convergent series. > [tan-1(2n – 1) – tan-1(2n + 3)] n=0

A: Telescoping series and converges for the series

Q: Determine whether the series E. (-2)" is convergent or divergent. If it's n=1 convergent, find its…

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Q: Which series converge, and which diverge? Give reasons for your answers. If a series converges, find…

A: Given Data The summation is:    Here,  Cos (nπ)=(-1)n There is geometric series of arn for with…

Q: ylor series ex

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Q: Can you convert any function to Taylor series give me example

A: Any function which is infinitely differentiable at a point aa has a Taylor series at that point

Q: Is this series convergent or divergent?

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

Q: Values of a series; Since EniXi = 180, x= 4.5 and Eni (Xi- x)2 =56, what is the coefficient of…

A: Given: The formula and calculations for s, i.e, sample standard deviation is as follows:

Q: Explain how to use a geometric power series to represent a function of the form f (x) = b/ c - x

A: given,       fx=bc-x

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

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Q: Discuss the similarities and differences between what it means for a sequence to converge and what…

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Q: Which series converge, and which diverge? Give reasons for your answers. If a series converges, find…

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Q: sin(3x²)

A: Given:            Function = sin3x2   power series for the function: sin3x2   A maclaurin series is…

Q: express (12+x)ln⁡(12+x) as a power series

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Q: An infinite series that represent periodic functions in terms of cosines and sines

A: We will find out the required solution.

Q: 3n5 Consider the series 2n5 + 3 n=1 The Test for Divergence tells us that this series: Explain.…

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Q: Can we apply Maclaurin series expansion for hyperbolic trigonometric functions? why or why not?

A: To show : Can Maclaurin series expansion be applied for hyperbolic trigonometric functions.

Q: A ball is dropped from a height of 75 feet, and each time it bounces it rises to a height…

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Q: sin n ") Ž -3 71 10) I 1=と

A: Here I am giving answer of first question if you want answer of remaining questions repost the…

Q: Use any method to determine whether the series converge: S Ink kVk

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Q: Question 1 Show that the convergence of a series is not affected by changing finitely many terms (of…

A: Image is attached with detailed solution.

Q: Determine whether the series converges or diverges. Explain your answer. 7 + sin(n) n = 0

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Q: (x +1)" 2" (n+1)

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Q: The sequence {n sin n3= If the sequence converges, find its value; if it diverges, enter DNE in the…

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Q: 100 500 2500 20 Given the series 9 81 729 6561 Does this series converge or diverge? O converges O…

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Q: 1) Š(-1)"- n² 2" n=1 a) Show that the series is convergent.

A: We have to show that the series is convergent.

Q: Determine whether the series is convergent divergent.Write the or exact test that you Use. Cos Cn)

A: The given question is related with convergence of series. Given the series ,…

Q: Which series converge, and which diverge? Give reasons for your answers. If a series converges, find…

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Q: Use geometric series to convert 0.99999 to a rational number: 1. When expressed as a geometric…

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Q: How do you define a power series centered at x = a? and centered at x = 0.? Give an example of each.

A: We will define a power series with centred at x=a is

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

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Q: Find a formula for the power series of ƒ(x) = 2 ln (1 + x), −1 < x < 1 in the form Σan. n=1 2 1 + x…

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Q: What is the radius of convergence of a power series? How do you find it?

A: Here we have to define the what is radius of convergence and interval of convergence and how to find…

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

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Q: Please help. Find the values of x for which the given geometric series converges. Also, find the sum…

A: (a)Consider the given geometric series:

Q: Find a power series representation for the function. (Give your power series representation centered…

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Q: n +1

A: Alternating series: A series of the form {\displaystyle \sum _{n=0}^{\infty…

Q: Write the tangent sum formula?

A: The tangent sum formula is given by