State why the following intergral is improper and find the value if it is convergent: 2r (z² – 4) "

Q: Calculate whether it is convergent or divergent. (4x)2* x=1

A: Given series is ∑x=1∞(4x)2xexx2x

Q: (b) Use the Direct Comparison or Limit Comparison Tests to test the following integral converges or…

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Q: oblem 3. Use the integral test to determine whether Y converges or diverges.

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Q: 52n 5n +1 n=1

A: Given that:- ∑n=1∞52n5n+1To find:- chek whather the series is convergent or divergentSolution:-limit…

Q: Decide whether the following proposition is true or false. Provide a justification for your answer:…

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Q: Determine If the divergent FoIOLWng intergral is convergent and find its value· or S. i

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Q: if Xn is bounded, is Xn  cauchy ?  is Xn convergent?

A: Solution

Q: Are the following convergent or divergent? Show your work and state the reason 100 11) Ση n=0

A: The summation of n, n from 0 to 100.

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

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Q: Š V2n-5 n=1 n2- 3n +4

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Q: The following improper ategral(r- De **!dx converges to3e convergesO optich

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Q: 2n + 5 9n + 4 n=1

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Q: +o0 ΣΗ 1 -3 -1-n n=1

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Q: find the Limit of each convergenl 2n t 1 An = 1 - 3Vn

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Q: 8. 4+n2

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Q: 8. 27 n=3

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

A: Use Alternating series test, P- series test

Q: #2. Give a counter exa mple that (Sn) is bounded but not convergent.

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Q: Determine whether the following converges or diverges. 2n + 1

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Q: It can be shown that lim beb = 0. Use this fact and the integral test to show that k is convergent.

A: Given infinite series is: ∑k=1∞kek Integral test states that the given infinite series will be…

Q: 2n-1 3n+2n+1 n=1

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Q: +00 El-1)» (" – n)" 2η n=1

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Q: 2k と(+ 1) converges. Use the integral test to determine whether k-1

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Q: If limkoo ak 0 then Eak is convergent.

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Q: 1 -2 (x+1)²

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Q: Determine whether the following integral converges or diverges. Be sure to use proper mathematical…

A: We have to check the given interval is convergent or divergent.

Q: Determine whether the statement is true or false. dr is convergent.

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Q: etermine whether the following is convergent or divergent and j

A: Given that,

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: A) diverges B) converges

A: If the limit exists and is a finite number, we say the improper integral converges . If the limit is…

Q: +00 3 E(-1)"+1, n n=1

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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: converge to the same limit.

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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: /5 too dr Vx-1

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

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Q: 3D (2Vn +1)n

A: The given series is,∑n=1∞2n2+1n

Q: n=1 3" 2n2 M.

A: We shall use elementary knowledge of Series and summations to answer this question. Note that…

Q: Σ 1. 4n n=1

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Q: If 2(-1)" a, is absolutely convergente the n=0 na, is divergente. Select one: O True O False

A: Topic:- sequence and series

Q: Determine if the following is convergent or divergent: a dr

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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: If I want to show that >1 an is convergent, it would be appropriate to use the direct %=D1…

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Q: what is b? it is the same question as a, so what is the convergence of B?

A: We can solve this as follows:

Q: Determine if the following is convergent or divergent: I dr

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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: Is the Sertes ko convergend orcirergent Convergond.ordhrergent =1

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Q: 6n2 n

A: The given sequence be 6n2en To find it is convergent or divergent

Q: cos" (;) is absolutely convergent, conditionally convergent, or divergent. en?

A: