Does the series from 1 to  infinity of ((5n^3+n^2-15)/(n^3+2))^n converge or diverge by the root test?

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A: Solve the following

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Q: st to determine whether the series converges or 5k2 – 3k + 10k7 + 2k – k=1

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Q: Use a power series to test the series £ Un=nlogx for convergence,  where £ means summation

A: We are given the series,                           . Now, we need to check the convergence of the…

Q: Determine the interval of convergence of this power series: 1+ 2x + 3x² + 4x³ + 5x*+..

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Q: 4 n(n+1) nel

A: Given: ∑n=1∞1n(n+1)-4n

Q: The interval of convergence for a given power series is (−7, 5). What is the center of this power…

A: Given interval of Convergence for a given power series  is  (-7, 5) (.)  The radius of Convergence…

Q: (-1)r+1. n=1 と(-1)"+1 n2 2]

A: Topic:- sequence and series

Q: If the test cannot be applied to the given series, give a short reason as to why not. n + 5" Series:…

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Q: sin(n+ n 2/ un3D0 1+vn

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Q: Does the series from one to infinity of 1/((3k+1)(3k+4)) converge or diverge using the integral…

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Q: n(lnn)? W?

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Q: Prove that the Sum of Convergent. Series is ungue

A: prove that sum of convergent series is unique.

Q: Determine whether the series below is convergent or divergent (do refer to this or that test or…

A: A series ∑nan is determined to be convergent if limn→∞an=0. A series ∑nan is determined to be…

Q: 4. Show that the series " is Convergent, but the (-1) squence s not summable.

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Q: The interval of convergence for a given power series is (–7, 5). What is the center of this power…

A: The interval of convergence for a given power series is (–7, 5) Then  -7 < x < 5   - - - (1)

Q: Determine whether the series (sin 3n)" \ nn n=1 is convergent or divergent.

A: The question is about whether the given series is finite or infinite in which we have to find the…

Q: 6. Σ(-1)n-1 sin (2) n=1

A: Explanation of the answer is as follows

Q: Determine whether the Series is convergent diveryent.Write or the exact test that you Use. 1t2

A: ∑n=1∞(-1)n1+2nn

Q: (За — 1)" 5n Vn + 1 n=1

A: Given problem:-

Q: How to determine if the series, converges or diverges using only the convergence test?

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Q: 08. Σ 3n 1 Arcsin 2n n=1

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Q: 2. Expand 1 into a power series with center zero and determine the interval of 2 – 3x3 -…

A: We have to find the power series and determine the interval of convergence.

Q: Soru 5 Find the sum of the given series if it converges. (-1)",2n 4 (2n–1)! n%3D2

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Q: +oo Inn n2 n=2

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Q: 1 Express 3, as the sum of a power series with center zero. What is the region of 1-3z validity of…

A: Te power series of the given function about z=0 is  ∑ n=0∞3nzn  and validity  Region is…

Q: investigate a series for convergence with a common term an= arcsin

A: Fact (2) is called "limit from of comparison test".

Q: Let 2 (-1)** 'ak be a convergent alternating series with terms that are nonincreasing in magnitude.…

A: We have to find the upper bound for  error.

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: find the power seriess representayion and the radius of convergence

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Q: Determine if the series is convergent or divergent using any tests (comparison/root/ratio).…

A: ∑0∞(-1n-1n+1n5)

Q: Determine whether the series converges or diverges. 9- 2(-1)" Σ converges O diverges

A: solve the following

Q: Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine…

A: We know, if the function f(n) is positive, continuous and decreasing on the interval [k, ∞) and that…

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A: This is a problem related to series and sum calculation. Based on the available formula and method…

Q: Inn E-1 n2 =2

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Q: Is the series s in () divergent, conditionally convergent, or absolutely convergent ? CHinki himit…

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Q: Find the radius of con vigence and intervald convergen nce of the power Aerues series: in 5n

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Q: 6. If a series Lu, converges to the sum u then so does any series obtained from Lun grouping the…

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Q: Determine the series converges or diverges, and if it converges find the sum 4k-

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Q: Check the convergence of the series Σ tan

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Q: 5) (1+2x) Arcsin x

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Q: 7) Explain why the series converges or diverges: Ln =0 (Hint: Geometric Series)

A: Use Geometric series test which states that:         ∑ n=1∞arn converges if and only if…

Q: FORUM DESCRIPTION Σ 1 list all the possible tests that can be used to determine the convergence or…

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Q: Determine whether the geometric series is convergent or divergent. If it convergent find its sum.

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Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent.…

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Q: Tn+3)! 2+1 4. In+3)! lim %3D0 Let, Series (comverges b.

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Q: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 4 += +-…

A: Check series convergent or divergent. By using comparision test.

Q: Determine whether the series is convergent or divergent. ke-9k k = 1 To receive any credit, your…

A: I use limit test to check series converges or diverges