Consider the series > an where n=1 (-4n + 7)2n an = (-2n – 9)2n In this problem you must attempt to use the Root Test to decide whether the series converges. Compute L = lim Vlan n-00 Enter the numerical value of the limit L if it converges, INF if it diverges to infinity, MINF if it diverges to negative infinity, or DIV if it diverges but not to infinity or negative infinity.

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A: Given: ∑k=1∞k2k2-4k+7

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A: Given that: ∑n=1∞7(2n+5)n

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A: The given series is: ∑3nn=0∞ This is a geometric series with common ratio:

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A: Now, convert the above series to improper integral.

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A: Explanation of the answer is as follows

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A: Apply series ratio test and find whether the series is converges or not.

Q: Determine whether the series converges or diverges 00 2+4n (2 + n2)3 O The series converges by the…

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Q: 8. nx" 9. Use the Root Test to find the interval of convergence of the power series > If needed, you…

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Q: Consider the series , a,, where In(n) a, = (-1)"(mn) y" n In this problem you must attempt to use…

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Q: find if series diverges or converges. if converges, find its limit 1 Ln=1 Tn+ 6) (n+7)

A: Telescoping Series : A series is called Telescoping series if nearly every term cancels with a…

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Q: (7) Use the definition of convergence for a series to prove that 2 n2 + 4n + 3 n=0 converges. Find…

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Q: Vn +2 Use the limit comparison test to determine whether the series ) converges nª + 4 n=1 or…

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Q: (7) Use the definition of convergence for a series to prove that 2 Σ n2 + 4n + 3 n=0 converges. Find…

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Q: 3n+7. 2η 12) E-1 n En%=D1 4n+2

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A: Use the ratio test for checking the convergence of series.

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A: We have the given series is of the form

Q: Yo2n +5 The series Converges to 4 Converges to -1/2 Diverges Converges to 1/4 Converges to 1/2

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Q: Find if the series converges or diverges from n=0 to n=infinity (k*ln(k))/((k+1)^3)

A: Given data is: ∑k=1∞klnkk+13  To find the series converges or diverges. [Note that the index cannot…

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Q: Consider the series 3 4n n=1 Determine whether the series converges, and if it converges, determine…

A: The given series,           ∑n=1∞34n

Q: arctan(n) n2+1 Ln=1

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Q: k! Σ (2k)! k=0

A: Given series is: ∑k=0∞k!2k!

Q: Determine whether the series converges or diverges. 3n2 1 4n° + 3 n = 3 converges O diverges

A: Given query is to find the series converges or diverges.

Q: Determine whether the series converges or diverges. 1 Σ 3n + 2 n = 1 converges O diverges

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Q: Determine whether the series is convergent or divergent. k2 k2 k = 1 2k + 9 convergent O divergent…

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A: The series resembles 1/n^2. So, it is convergent.

Q: Use the root test to determine whether the series converges or diverges. If the test is…

A: CONCEPTS:

Q: Consider the series 00 n E In n + 2 n=1 Determine whether the series converges, and if it converges,…

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Q: Determine whether the series ∞∑n=1 1/(n+1)ln(n+1) converges or diverges.

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