If an| converges then diverges because for large n. Vn n=1 True False Reset Selection

Q: Discuss the Conditions foo which Foudies Segies is convergent?

A: Given: Conditions of Fourier series is convergent.

Q: 1 converges conditionally because lim 第-1 = 0. 2n n=1 True False Reset Selection

A: this is false becuse

Q: is it absolutely convergent, conditionally convergent, divergent, or cannot be determined

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Q: a) On = Select correct it converges to 2 converges to I Converges to O • Converges to diverges to…

A: a). Given an = 2nn2nn! As n! < 2n   for all n > 1 So limn→∞an = limn→∞2nn2nn! = ∞ Hence…

Q: 00 Show that converges if [r| < 1. п: п

A: The given series is

Q: (4n)! an (4n – 1)!

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Q: D) { (-)"} [Select] [Select] converges to 2.

A: Please see the below picture for detailed solution.

Q: converge absolutely, non-absolutel

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Q: Find the limit numbek of the fallawing Sequencer er divergente and which of them is convergent 4-…

A: To find the convergence of the sequence and obtaining the limit

Q: Which converge and diverge?

A: In this question, we have given four multivariable functions. for each of them, we have to check the…

Q: 1 Is (-1)"- conditionally convergent, absolutely convergent, or n In n divergent?

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

A: For the solution follow the next step.

Q: Test the convergency o f Stan ("

A: According to the given information, it is required to test the convergence.

Q: Suppose Y, a Poisson(0) as n → ∞. Binomial(n, 2) for n = 1,2, 3, .... Show that Yn converges in…

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Q: The interval of converge Use your own wo each step) that yo

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Q: Σ Show that n2 + 1 converges/diverges n

A: The given series is: ∑n=1∞nn2+1 Let  an=nn2+1,n≥1    =nn21+1n2   =1n1+1n2 And, bn=1n

Q: Corver Is absdutely contergent, Conditionally Convergent, on divergent

A: Use Alternating series test, P- series test

Q: Show that the sequence (x)=(1/√n) convergence.

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Q: Let fn be a bounded sequence of functions uniformly convergetn to f. Prove that f is bounded as…

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Q: H) IM:

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Q: Show that every convergent seapuence is Cauchy but the convesse is not true in general.

A: A sequence is said to be Cauchy if there exist a natural number N and a small positive number such…

Q: 2 n 1 o Show that + converges/diverges n-

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Q: A sequence of functions that converges pointwise on [0, ∞0) but does not converge uniformly [0, 0).…

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Q: #6) Deler mine whether converges diverges, Calculatk limit an n+3

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Q: an2

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Q: Determine if the given is convergent or divergent. Indicate what test is used In n 1. n=1

A: To determine that the following is convergent or divergent  ln2nnn=1∞ ∑n=2∞ln2nn Root test: If…

Q: converge absolutely, converge conditionally,or diverge?

A:

Q: (#3) Determine if an converges or diverges. If it converges then what (n+1, does it converge to?

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Q: What is the convergency interval of (nl)*3" M(2n)! www n ww at. O a. [-4/3,4/3] O b. (-2/3,2/3) О…

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Q: Use the Raho Test to determine whether thc serics is convergen Or divergent oo(-3 n 0

A: Here, the general term of series  an is shown on board. Forstly, we calculate next term and…

Q: Determine if the series converges. If it converges find the limit. (In n)2 an

A: Series integral test:   The series ∑nan is converges if the integral ∫n f(n) dn converges and…

Q: Σ converges/diverges N! 9) Show that

A: Ratio test

Q: an conditionally converges then Jan] converges. n=1 n=1 True OFalse Rationale: Reset Selection

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: Suppose that p(x)=an" converges on (-1, 1], find the interval of convergen n=0 8 left end included…

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Q: Series that diverge absolutely may conditionally converge O True O False

A: Ans is   True.

Q: If \( \{a_n\}\)  is decreasing and bounded below then it is convergent.  true or false?

A: Monotone Convergence Theorem : Every bounded monotone sequence is convergent.

Q: a) an en 3n

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Q: .Use the Monotone Convergence Theorem to show that the (2n)! {a)" is convergent.

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Q: converges, because lim n! 2(n+1) n! = 0. (n + 1)! 2* n+00 True False Reset Selection

A: The given statement is true. Use the ratio test to find the evaluate the nth term.…

Q: IF in a normed space X, the absolute convergence of every series always implies convergence of the…

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Q: =) Show that converges/diverges n-1

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Q: If 21ak converges then E,ak, converges for any ak subsequence of ak.

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Q: Test E(-1)" for convergence or 3n+2 divergence.

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Q: Show that Seauence Converse is not tade in gehQlali every Convergent is čauchy But

A: We need to prove that every Convergent sequence is Cauchy but the converse is not true

Q: n! 1.3.5•••(2n-1) -} +∞ n=1

A: The question is solved by monotone convergence theorem. The sequence is decreasing and bounded below…

Q: If {an} converges and {bn} diverges, then {an + bn} converges. Is this ture or false. Please show…

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Q: Which of the following can the divergence test be used on to directly establish converges or…

A: we have to test whether the given series is convergent or divergent by using directly divergent test

Q: The sequence fn(x) = is 72 Select one: a. diverges Ob. converges uniformly but not pointwise C.…

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Q: EXE CISES Prove that every uniformly convergent sequence of bounded functions is uni- formly…

A: Use the definition of sequence of functions to solve this problem, as mentioned only first, in next…