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

Q: 8. 1 Σ 7n + 10

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Q: 1 converges or diverges. As part Let b be a real number with b > 1. Determine whether 1+ bk k=0 of…

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Q: Test for convergence 1 n=1n(a+2) n=1 N

A: The series is convergent if and only if the sequence of the partial sum is convergent. The series of…

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

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Q: Discuss the Convergence a 2 e¹ M8 n=1 SH n

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Q: 00 っ 6)2 _タ? n=ノ

A: Given that, ∑n=1∞enn2    Let ,an=enn2 limn→∞an=limn→∞enn2 Applying L'Hospital rule,…

Q: (X + 2)" 2) Find the interval of convergence for N! N

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

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Q: quence (x₂) satisfying A sequence 1 0≤x≤. n where Σ(-1).x, diverges.

A: Given that the sequence xn satisfying 0≤xn≤1n. We have to determine whether the series ∑-1nxn…

Q: (-1)" converges conditionally. Inn Show that n=2

A: For the solution follow the next step.

Q: (-1)"+l2nx" n2 +3 Determine the interval of convergence of n=1

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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: 10) Does the sequence an = √n² + 3n - n converge or diverge? Explain

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Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A: Given that  F is the vector filed orientation surface s  To find the fulx of the vector

Q: Vn +1- n –1 n=1

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Q: Q.2) Determine of each point convergens or diverges: (-1)"(3n)!/ /n! (n + 1)! (n+ 2)!

A: determine whether the series converges of diverges (i) ∑n=0∞-1n3n!n!n+1!n+2! we will use ratio test…

Q: (X + 2)" 1) Find the interval of convergence for N!

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

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Q: If akxk converges for x = -8, then which of the k=0 following must be true? I. ax* converges for x =…

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Q: 9) n+3"

A: Comparison test for series of positive terms states that, If an, bn are two series such that…

Q: What does Ek=1 converge to? Ak+11 k+12.

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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: B) > n! (4x – 6)" is convergent for x = n=1

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

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