. Determine the interval of convergence for the following power series. Your work must name the test(s) you use as well as show all the key details of applying the test(s). (a) ;(x+2)". n=1 (b) (n + 1)!(x + 1)". n=1

Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at…

A: using ratio test we can find the interval of convergence

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Q: Find the interval of convergence for the given power series. Use interval notation, with exact…

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Q: To test this series for convergence n° + 3 п4 — 4 n=1 You could use the Limit Comparison Test,…

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Q: (n!)² ". Show your work. (5) Find the interval of convergence of the power series (2n)!

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

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Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at…

A: The given sequence is ∑n=0∞-1n+1n+6xn=∑n=0∞an

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A: ∑n=2∞1n-1

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A: To begin with the p-series,

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Q: Determine the interval of convergence for the following power series. Your work must name the…

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Q: To test this series for convergence n' + 2 You could use the Limit Comparison Test, comparing it to…

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Q: Find the interval of convergence for the given power series. Use interval notation, with exact…

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Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at…

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

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Q: why does power series always have radius of convergence and interval of convergence?

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A: Recall the Ratio test: Let ∑an be any series and suppose that limn→∞an+1an=L. Then, i) The series is…

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Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at…

A: The series is given as ∑n=1∞n!(x+4)n1·3·5···(2n-1) Hence the nth term is an=n!(x+4)n1·3·5···(2n-1)…

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A: the given series is ,  ∑n=1∞ 10n4+9n

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A: the series conditionally convergent