10) (9.) Determine the convergence of the following. 00 3n n2 n=1 +n (2n)!

Q: tan (x) +n In(n+2) 04: Determine the convergence of , on A=[0,+).

A: given fn=∑n=1∞tan-1xx2+n2lnx+2  on A=[0,∞) claim- to determine the convergence

Q: 2. Find the interval of convergence of the series (n + 2)(x + 3)²n+2 2n

A: Here an=n+2x+32n+22n. The series converges if limn→∞an+1an<1

Q: Show that the series Ln=l 12+2z10n-5z"ª –3z+2;10n converges absolutely for |리 < 1.

A: The series ∑n=1∞an is absolutely convergent if the series ∑n=1∞an  Ratio test:  The series ∑n=1∞an…

Q: Find the interval of convergence of the series. 7x" Σ n = 1

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Q: 4n+3 Examine the convergence of the series En=o,AT by applying limit comparison test.

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Q: 00 Suppose that p(r) = > anc" converges on (-1, 1], find the internal of convergence of p(3x – 7).…

A: Given that ∑n=0∞anxn converges on (-1,1]  To find the interval of converges of p(3x-7)

Q: Find the interval of convergence of the series. (x - 4)n Σ 8+ 5n n=0 45 19 <x< 8 -1 < x< 9 -1 sxs9…

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Q: How would I find if the sequences an=nπ cos(nπ) and an= (n2)(1/n) are convergent/divergent?

A: To examine the given sequence regarding convergence, that is study the limits as n tends to infinity

Q: 1. Find the radius of convergence of (-1)" n! (3x + 1)" n=1

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Q: Find the interval of convergence for 2 (k + 5) 2* а) O[-3, 3] b) O[-1, 1] c) O (-2,2] d) O[-2, 2) e)…

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Q: Find the interval of convergence of the series. (3x)" 2" n=1

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Q: 2. Find the region of convergence of the series (3r)" +2

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Q: 4. Find the radius of convergence and interval of convergence for the following. (х — 2)п 2n (2n)!…

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Q: Find the interval of convergence of 5 (x - 9)" In (5n) n=2

A: Solution of question is written in below steps.

Q: Find the interval of convergence of the power series: ∞ n [²(+1²] (x + 1)n 1)"] 2n n=0

A: To find the interval of convergence.

Q: 2. Find the interval of convergence for the series. n=1 (x - 7) n n5n

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Q: Q4/ Use Partial Sum Test to check the convergence of the following se 00 (-1)" n=0 Ans./ Diverged

A: Topic- convergence divergence

Q: Q4. Test for convergences of the following: 7 図t X 2n=2 10-1 Vn+1-Vn 131 Vn2+n

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Q: Find the interval of convergence of the series. (x-1) 5n+ 4 n=0

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Q: 2. Consider the power series 1 (-1)*+1 (x-5)" 4nn What is the center ? What is the interval of…

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Q: (b) Analyze the convergence of (-3)" n25n n=1

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Q: Q4. Test for convergences of the following: 7. 因 ニ2 +00 10n-1 Vn+1-vn X 2n=1 n%3D1 Vn2 +n

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Q: 5. Determine the convergence set of the following power xn+1 Zn=1 (п-1)!

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Q: Show that the interval of convergence of the series (-1)"(2n + 1)²x" is the interval (-1, 1).

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Q: Q3: Show that 3(2)n+2 3(2)n+2 is convergence and En=0 5n Zn=0 5n 20.

A: Please refer to the image below.

Q: 2. Determine if the series n n4 + 1 n=1 Σ (-1)3n converges or diverges. 3. Consider the power series…

A: Series and sequences

Q: Check the convergence of J (x-2)²

A: Let x-2=tThen dx=dti.e.∫-∞11(x-2)2dx∫-∞-11t2dt      [x=-∞, t=-∞-2=-∞]  [When x=1, t=1-2=-1]

Q: Find the radius of convergence for: (2n) !æ" n=1 n2n

A: Recall: Radius of convergence: Consider the power series           ∑n=0∞an(c-a)n, then the radius of…

Q: 1 [3x+2]n 00 2n+1 -5 |

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Q: Find the interval of convergence of the power series Σ (х — 3)" 2" /n n=2

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Q: Q4. Test for convergences of the following: 7 因 + 2n=2 10n-1 Vn+1-vn X En=1 Vn²+n

A: a∑n=2θ710n−1Using Ratio TestL=limn→∞an+1aniIf L&lt;1,then the series converges absolutelyiiIf…

Q: Suppose that p(æ) > anx" converges on (-1, 1], find the internal of convergence of p(6x – 9). n=0

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Q: 1. Show that fn(x) →0 for each x E [0,1]. -> 2. Determine whether or not the convergence is uniform.

A: In this question, we find the limit of the sequence of function and in the second part, we use Mn-…

Q: Find the interval of convergence of the series. (x-5) 5n+1 n=0

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Q: 00 ·E(-1)"- 14. n=1

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Q: Find the interval of convergence of the series. (3x)" * Σ n2. 10" n=1

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Q: 6.4 Suppose that n =0 anx" has an interval of convergence of (-1, 1). Find the interval of…

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Q: Find the interval of convergence for the power series (2) 4)" 5n n=2

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Q: 04: Determine the convergence of tan¹(x) x²+n²In(n+2) , on A = [0, +00).

A: We have to determine the convergence of the given series of functions ;   ∑n=1∞an = ∑n=1∞tan-1xx2+n2…

Q: Find the interval of convergence of the series. (X- 4)" %3D 7+4n

A: Given:∑n=0∞x-4n7+4n

Q: 1. Show that the sequence ((nx - - 1/n)e n) converges uniformly on [0, 0). (15 points)

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Q: 12. Determine the radius and interval of convergence of 8 k=1 (-1)kk²(x-4) k 3k

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Q: 2" Зп+2 n=0

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Q: 5. Show that the sequence Pn = 1 converges linearly to p 0, and the sequence Pn = 10-2" converges…

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