Σ (-1)** In+15 a. Absolutely Convergent b. Conditionally Convergent с. Divergent

Q: nx (a): Show that the sequences is not uniformly convergent [0, 00]. on '1-n²x2

A: Given the sequence of function fnx=nx1-n2x2, x∈[0,∞) Now , for x=0, the sequence is 0,0,0,.... this…

Q: If lim an 1 then n00 Σ an n=1 converges O diverges O may or may not converge

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Q: n² – sin(n) nº + n² 1. Determine whether is absolutely convergent, conditionally convergent, or…

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Q: I. Consider an = V4n² + 3n – 2n for n >1. 1. Determine if {an}-1 is convergent or divergent. 2. Is >…

A: Simplify the expression of an. Multiply and divide the given expression of an by 4n2+3n+2n to…

Q: The series Σ 6( − 1)*0.2-1.9/k○ diverges converges. k=0

A: We use ratio test to find the desired result.

Q: n=1 (ii) Give an example such that a, converges conditionally and diverges. IM:

A: Please see the below picture for detailed solution.

Q: 52n 5n +1 n=1

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

Q: 1 n=2 n(Inn)P -4

A: We need to find the value of p for which series convergent.

Q: /2n?

A: The given series is: ∑n=1∞(-1)n(-1)n2n2+5=∑n=1∞(-1)2nn2+5n2=∑n=1∞1n2+5n2

Q: (-1)^ – 1 Vn - 1 | Σ n = 2 convergent divergent

A: Please rate

Q: (-1)* Lk=3 In k absolutely convergent, conditionally convergent, or divergent? 100

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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: tion 35 Suppose lim an = 00 and an1> a, > 0 for all n> 1. Which of the following statements must be…

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Q: If lim =c>0 , then b, , a, both convergent and both divergent.

A: By limit ratio test we know that if above condition is true then either both series diverges and…

Q: Š V2n-5 n=1 n2- 3n +4

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Q: Petermine whether (-1)k converges absolutely, converges conditionally, kl/2 k=1 diverges. or

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Q: 1. Determine whether n² – sin(n) is absolutely convergent, conditionally convergent, or diver n6 +…

A: Solve the following

Q: +o0 ΣΗ 1 -3 -1-n n=1

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Q: 8. 4+n2

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Q: 3 - If E is convergent, find its sum. z=1 en n(n+3)

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Q: 3. Determine whether E (-1)" converges absolutely, conditionally or diverges. Explain.

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Q: Q1-) Determine whether the following functions are convergent or divergent: 1 1- En=1 ((3n-1)*/…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If an> 0 and Σ an converges, then Σ(-1)"an converges.

A: We have to check wheather it is true or not

Q: d) Determine whether ) (an + bn) is convergent or divergent. n=1

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Q: Determine if the given is convergent or divergent. (x²+1)² n Zn=1 (n²+1)²

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Q: E (1- nsin-) converges n = 1

A: Series convergence test problem.....

Q: 1) (am) is not convergent but (a,(a, - 2)) is convergent.

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Q: Σ s2 an convergent or divergent?

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Q: , 2η En=1 3 er

A: Given series is ∑n=1∞ n2nen3. Here, an=n2nen3.

Q: 9. Determine whether the following is convergent or divergent +(-1)"+1 n! 2n 2e

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Q: 6 Let an 3n + 1 (a) Determine whether {a,} is convergent. convergent O divergent (b) Determine…

A: We can find the answer as below.

Q: 2)(A) Determine of each point convergens or diverges: (1) 1 (215) ² n(5) 2n+1) (-2)"(x-3)" ΩΣΗ στο…

A: Note: since you have posted multiple questions. As per our guidelines we can solve only one problem…

Q: +00 El-1)» (" – n)" 2η n=1

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Q: 4n Determine whether {} 5n+1 is convergent or divergent.

A: A sequence {an} is convergent if limn→∞an=l, where l is a finite real number.A sequence {an} is…

Q: n = 1 Vn lim n-00 converges O diverges

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Q: n2 3" 1) > 6n+1 n=1

A: Given query is to find the series converging or diverging.

Q: 8. n2- 1 n = 2 convergent divergent If it is convergent, find its sum. (If the c

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Q: If lim=c>0, then both convergent and both divergent. ylgn O Ihi O

A: If limn→∞anbn=c>0, then ∑bn,  ∑an both convergent and both divergent. (a) True (b) false

Q: show : ΣΣ - a"d, (x - a)" | n=0 m=0 is convergent,

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Q: ax Examine the convergence of , where a>1. x (log xy" +1

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Q: 4n Determine whether Σ: 5n+1 is convergent or divergent.

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Q: dx is convergent V2 1 True False 1, 8.

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Q: If lim,→00 an 0 then an converges. Select one: O True False

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Q: ii. ) -3(n+1) -3n e n=1 If it converges, state the number that it converges to. If it diverges to,…

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Q: Determine whether the scries is absolutely convergent, conditionally convergent, or divergent. (a) E…

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Q: Σ 1. 4n n=1

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Q: N + 1 2N 2) Show that converges/diverges. N-1

A: The given series is: ∑N=1∞N+12N+1 Let. aN=N+12N+1,N≥1

Q: n! Determine whether E- converges or diverges. Zn=0

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Q: (금) +00 Σ -3 - n el-n n=1 convergent divergent

A: