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

Q: {B"}-o; ß E (-1,0) A-Converges B-Diverges C-Absolutely converges D-Conditionally converges

A: According to our answering guidelines we can answer one question at a time, therefore I have…

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: Σ 2n n? + 2n h= 1

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Q: - Find the interval of convergent for : 2n 2 2n! n=0

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Q: Jlgu (-1)" +1 Σ (3x)" What are all of the values of x ,such that 00 converges? n=1 x>02 C) x>3.3 O

A: Using ratio test the condition of convergence is:…

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

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Q: B. Give an example for a function which is a pointwise convergent but not uniform convergent. (Prove…

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Q: 1 E(-1)"+1, ( n + 1 ) . 3η n=1

A: To find whether converges or diverges

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: m-1 -4 m3D1 converges.

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

A: Please rate

Q: xp Vx(x + 5) converges O diverges

A: CONVERGES

Q: リT ヒ-」

A: Consider the given series ∑k=1∞1k1π

Q: a n+1) %3D 2n Ans. Converges, 6)

A: Since you have posted a multiple  question according to guildlines I will solve first (Q6) question…

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: -6 Σ n(n + 2) n = 1 convergent divergent If it is convergent, find the sum. (If the quantity…

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Q: n 2n – 1 n=1 Does this diverge or converge? Explain your answer.

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Q: Σ (-1)*2* Use the Ratio Test to determine whether converges absolutely diverges. or k! k=1

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Q: 2" n3 Σ 4"+1 n=1 is convergent or divergent.

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Q: 8. 4+n2

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Q: n" 3) > (-3)2n n=1

A: We apply here root test.

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

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Q: Determine whether E=1(-1)"+1. 2n converges or diverges. If it converges, find the sum. 3n

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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: etermine and justify if ∞ In(x) k=2 (1+k) ³/2 converges or diverges.

A: given series ∑k=2∞ln(x)(1+k)3/2

Q: (-1)+ (x+2)" Example / Find the interval of convergence of E-

A: Here we have to find the Interval of convergence ,  ∑n=1∞(-1)n+1(x+2)n2n×n

Q: 1 1. Determine whether I = dr converges or diverges. If it converges, find its value. (6 13/17

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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: K3-2

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Q: 1 1+ 2/2' 3/38 1 1 + 1 + ... 5/5 +

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Q: Σ (x – 3)" 2" +1* Determine the interval of convergence of n=1

A: Given:

Q: 8 csc(x) dx 7/2 O convergent O divergent If it is convergent, evaluate it. (If the quantity…

A: Converges and diverges of series

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: ∫0∞eax dx converges for a<0. Now, ∫0∞eax dx=eaxa0∞=1ae-∞-e0=1a0-1=-1a

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

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

Q: DA. The sequence {(- 0.002)"} converges by oscillation to the limit |

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

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Q: Determine whether E1(-1)" sin n3 is absolute convergent, conditionally convergent, or %=D1…

A: We have to find the series test

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

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Q: 1 (V3)" n = 0 convergent divergent If it is convergent, find its sum. (If the quantity diverges,…

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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: Inx? x² –1, 2 x=2 A-Converges B-Diverges C- Absolutely converges D-Conditionally converges 8.

A: In both cases we use comparison test.

Q: ) De termine the given Segunence converges or diverges: 8.

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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: 4. Determine whether the scrics is absolutely convergent, conditionally convergent, or divergent. k…

A: Here we have, ∑k=1∞-1kkk3+2=∑k=1∞-1kak

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

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Q: (-1)"(7n + 1) Does En=1 converge or diverge? (3n + 1)

A: Alternating series test: If infinite series is If any of these two conditions does not hold, then…

Q: 3k 5- 2k+1 k=1 2 1. Does converge? If so, what does it converge to? If not, justify.

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.