Show all of your work and mention what formula/theorem/test you are using. You can use DESMOS to check your work, but a picture does not count as a proof. Use either direct or limit comparison test to find out whether the following series converge or diverge. You must give adequate explanation for any claim you make. i sin²i 1+i (a) (b)

Q: Find the radius of convergence, R, of the series. R = 00 Σ n = 1 I = 1 3 5 xn ..... (2n-1) Find the…

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Q: Find the radius of convergence of the power series. (If you need to use co or -00, enter INFINITY or…

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Q: sin -:

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Q: Use Taylor expansion to answer several questions:

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Q: Determine whether the series converges or diverges. Indicate the type of series or test(s) that are…

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Q: En=1(-1)"+1 tan-1n a.

A: At n -> ∞  The nth term will be    Tn  =  limn→∞-1n+1tan-1n  =  tan-1∞ limn→∞-1n+1 =  π2…

Q: Determine if the following series converges. Explain your reasoning. sin(k) k2 k=1 8WI

A: Calculating the limit of the series as k tends to infinity.

Q: Find a formula for the power series of f(x) = 4 ln (1 + x), –1 < x < 1 in the form a,. Hint: First,…

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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: Find a power series for the function, centered at c. 8 5-x £( n = 0 f(x) = C = 1 Determine the…

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Q: For this problem, type your answers directly into the provided text box. You may use the equation…

A: The root test is a simple test that tests for absolute convergence of a series, meaning the series…

Q: 1) Find a power series representation for the function and determine the interval of convergence.…

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Q: Show all of your work and mention what formula/theorem/test you are using. Find the interval of…

A: The power series is  ∑n=0∞ (2x-1)n5nn

Q: 2k–1 sin? k 1+k3 k=1

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Q: Find the radius of convergence, R, of the series. R = 0 Σ n = 1 I = 1.3.5 xn ..... (2n-1) Find the…

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Q: Use the Root Test to determine the convergence or divergence of the series. (If you need to use co…

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Q: Find all values of x where the given series converges. 9" x" (n + 1) n + 9 n=1 Answer: Note: Give…

A: Given ∑n=1∞9nxnn+1n+9

Q: Use the Geometric series, differentiation and integration of power series to find power series…

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Q: x+2 f(x)= 2x – r+1

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Q: Σ sin cos(n) п

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Q: Determine whether each of the following series converge or diverge. State the name of the test you…

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Q: > ke 10 k=1

A: The given series,      ∑k=1∞k e-110k2

Q: Determine whether the series is convergent ordivergent. the exact test that you Use. 00 Sinl 2. nこ1

A: To determine whether the given series is convergent or divergent.To write the exact test that you…

Q: (b) Use the power series of sin x to evaluate the following indefinite integral as an infinite…

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Q: +oo El-1)» (" – n)" 2" n=1

A: The given series to be tested is  ∑n=1+∞-1nπn-nn2n.   Here, we will use the Root Test: If series…

Q: 2. Use the integral test to determine whether the following series converges or diverges. Make sure…

A: Solution is given below:

Q: Find a power series for the function, centered at c. F(x) = 1. c = 2 7 - x f(x) = 5 n = 0 Determine…

A: We have to find Power Series and Interval of Convergence.

Q: Find a power series representation for x2cos(2x) and then by differentiation, show tat the equation…

A: Power series exaption of the function

Q: Find the radius of convergence, R, of the series. xn + 6 7n! Find the interval, I, of convergence of…

A: For the series ∑an radius of convergence we will follow the following stepslimn→∞an+1an&lt;1  and…

Q: Find all the values of x such that the given series would converge. Note: Give your answer in…

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Q: a) Make a conjecture about the convergence of the series, cos E by considering the local quadratic…

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Q: 00 2" (x + 2)". Σ n = 1

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

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Q: Find the function to which the given series converges within its interval of convergence. Use exact…

A: Sum of infinity GP

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

A: We have,

Q: Consider the series: p Use the Integral Test to determine whether this series converges or diverges.…

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Q: Using Direct Comparison Test (DCT), the following series : 10 + sin(n²) n4 n=1 is convergent is…

A: Let an=10+sinn2n4 Then using triangle inequality  10+sinn2n4≤10n4+sinn2n4…

Q: Show all of your work and mention what formula/theorem/test you are using. (a) Determine whether the…

A: (a) Given series, ∑n=2∞cosnπsinπn2 We need to check whether the series converges absolutely,…

Q: petermine whether the Series is convergent divergent.Write the or xact test that you Use cos Cnt)

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Q: By manipulating a geometric series, determine a closed form power series for each function below.…

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Q: 1 Σ sk[Iin(k)]* k=3

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Q: tänh y - x Series to find limit

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Q: Determine Whether the Series is convergent ordivergn. Write the exact test that you US e, 2n-1 Sin T…

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Q: Find the first 4 terms of Maclaurin series for f(x) = sinx+ ln(cosx). Find the error we make when we…

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Q: (х — 3)" 3" n=1

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Q: 7. Find the power series expansion for the function and simplify: e* f(x) = 1+ x2 And then find its…

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Q: Find a power series for the function, centered at c. 2 f(x) 3x + 2 c = 3 f(x) n = 0 Determine the…

A: Given, fx=23x+2,  c=3

Q: 6 Σ. n+sin(n 100 m=1 n2+100,000

A: note  series ∑n=11np is convergent if and only if p&gt;1

Q: 'n – 1 sin \n + n=1 8

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Q: sin(n) n2 Determine if the series, is absolutely convergent, conditionally convergent, or divergent.…

A: Given:         ∑n=1∞sin(n)n2    If sum of an converges ,then sum of an converges.…