Find the coefficient of x12 in the power series of each ofthese functions.a) 1∕(1 + 3x) b) 1∕(1 − 2x)2c) 1∕(1 + x)8 d) 1∕(1 − 4x)3e) x3∕(1 + 4x)2

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A: We will apply Ratio Test to check for the convergence of given series:Ratio Test: Suppose we have…

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A: Given a series. We need to verify that it diverges. Let's prove it.

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A: Since you have posted multiple questions we will solve the first question for you. If you want any…

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A: The series is given as , ∑k=1∞1k+9 Determine whether the series converges.

Q: 00 1. is converg if the series In(3n) 71-2

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A:

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A: Given series is ∑n=4∞lnn2.

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A:

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A: We have to find if the given series is absolutely convergent, conditionally convergent or divergent.…

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A: We will do Ratio test.

Q: Suppose that a is a number such that -9 an+1 -3)2n+1 n=0 convergent or divergent? If the series is…

A: given sequence is                                                      ∑n=0∞an+1(-3)2n+1

Q: 19.Use geometric series to represe nt the FuncHion n F(x)= 5 as power こ 3-X series about

A: Solve the following

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A:

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A: Given,   We have to check whether the series convergent, divergent or conditionally convergent.

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A:

Q: A-Show if the series is convergent or divergent (2n)! 2n n²

A: The given series is ∑n=1∞(2n)!n2n

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A:

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A:

Q: Σ n² – 3n + 2 n=3

A: Explanation of the answer is as follows

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A: Topic = Series

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A: we have∑n=1∞4n+34n+1

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Q: Verify that the infinite series diverges.

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Q: b. Write the power series using summation notation. f(x) = e*, a = In 18 %3D

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Q: determine if the series is convergent or divergent

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Q: 3. Determine whether each geometric series converges. If the series 7n+1 2n converges, find the sum.…

A: Let's find.

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Q: Determine whether the series is convergent or divergent. 00 In(n) n = 1

A: