Use the root test to find the radius of convergenc n n Σ (m+-+²1) ² = xn 9n +4 n=1

Q: The sequence {(-1)"*'. 2},=, is Select one: a. Divergent b. Convergent

A: Sequence problem....

Q: Q1/ is the sequence {a,) converge > sin n

A: We have to find given sequence is convergent or not .

Q: Does it converge: ∑(sqrt(n+1) - sqrt(n))/sqrt(n2+n) if so what is the sum (show steps please)

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Q: p for which In (n) Comvenges

A: Given∑n=1∞ln(n)np

Q: Determine whether each of the following sequences convergent, justify!, is (@) (X₁) where I : =…

A: (a) The given sequence is . Since  is a bounded sequence and .Then Hence the sequence  is…

Q: (x + 4)" n(n + 2) n=1

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Q: Suppose (xn) converges, and let K be a positive integer. Now create a sequence (yn) by changing the…

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Q: find if it converges ∑∞ n=0((4n)!(1103+26390n))/(3964n (n!))  (show each step please)

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Q: Q3/ Generate and plot the following sequence over the indicated interval. Provide the scripts used…

A: Given recurrence relation is  yn=10.5-0.2n-7un+20-un-10cosπn2un+10-un-20             (i) It is known…

Q: show if it converges or diverges ∑(sqrt(n+1) - sqrt(n))/sqrt(n2+n)

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Q: Prove, using the e−N definition of a convergent sequence, that the sequence  (1 + 4n)^2/1 − 3n −…

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Q: 3. Determine if the sequence xn = 47² is convergent or not and find its limit if it exists n²+1

A: We want to find the given sequence is convergent or divergent.

Q: compute the 9-th convergent to √29.

A: We need to find the smallest positive integer solution to  or compute the  convergent to .We will…

Q: 1² + 11 For what value(s) of n, the integral dr converges? Justify In + 8x2 + 2 your answer.

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Q: (3n)" (2n + 50)" n=1

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Q: Determine of each point convergens or diverges: (-2)"(x-3)" (3) √(n+1) M=O

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Q: al = /3 , a2 = V 3- V3 , V 3 - V 3+ v3+ .. + V3 ....

A: We have to find the limit of the sequence…

Q: Solve Σ 0 to ∞ ((n! • x^n)/ n^n) for x = e and x = -e and explain whether each point converges or…

A: Solve for x = e and check whether it converges or diverges as follows.

Q: 4. Show that the sequence {fn}, where fn(x) = xER 1+n°x*' is point-wise convergent but is not…

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Q: Identify two subsequences of ((−1)^n + 1/n) which converge to different limits. You should include…

A: Let the given sequence is Sn=-1n+1n We have to find two subsequences of given sequence that converge…

Q: Is the sequence (N SIN N) properly divergent Is the limit +∞ or -∞0 ?

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Q: Vn +1- n –1 n=1

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Q: Is the sequence divergent or convergent? {vn - vn+1}

A: n  - n+1 =(n  - n+1) (n  +n+1 )/(n  + n+1) n  - n+1  = (n - n - 1)/(n  + n+1)  n  - n+1  =  - 1/(n…

Q: Find the limit of the sequence or determine divergence {2n+13-n}

A: Given sequence {2n+13-n}={un} (say)

Q: .(-1)*, x+4). Remember to consider the endpoints Determine the interval and radius of convergence…

A: Given ∑n=1∞-1nn.3nx+4n Ratio test- If limn→∞an+1an=L, then the series ∑n=1∞an converges if L<1…

Q: Determine whether ∞∑n=1√n / 2n2+n+5 is convergent.

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Q: (6n² + 1' Given the sequence prove that it is monotonic and bounded. Зп2 — 1 n=1

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Q: Verify that x = 1/a is a fixed point of the function g(x) x(2 ax). Determine the order of…

A: To show that x = a is a fixed point of g(x)=x( 2-a x) it is sufficient to show g(a)=aand if we can…

Q: show that this converges 2srt(2)/(9801) ∑∞ n=0((4n)!(1103+26390n))/(3964n (n!)) = 1/pie (show each…

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Q: Let a1 = sqrt{2} and ak+1 = sqrt{2+sqrt{ak}}, k = 1,2, ... Show that the sequence {ak} is convergent

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