If dn conditionally converges then Jan| converges. 2=1 2=1 True False Rationale: Reset Selection

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: sin N 8) Show that converges/diverges.

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Q: Determine whether or not the series of functions {Sn(x)} = {> xk-1} converges uniformly on [-a, a]…

A: We shall use the basic knowledge of power series and notions of converges and we shall use the…

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: 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 power series > (2 – x)' converges absolutely on the interval r=1 (1, 3) [1, 3] (-2, 2)

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Q: The following improper integral (7x-5) (x+3)(x²-x+1) converges to In(2) diverges This option This…

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Q: 1. Vn2+n-1 n=1 O converges diverges

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Q: ーuトー 1+uド or diverges Converges

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Q: cot(8)de is a) converges to - 1 b) converges to - 2 c) converges to -n d) diverges e) None of all

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Q: The series: (-1)" tann n=1 Da. converges absolutely Db. converges conditionally Dc. diverges 8.

A: Answer is following.

Q: Ee whether or not fn converges uniformly nclusion. b) (0, 1)

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

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Q: 4. Does cosnx uniformly converge in [a,b] c (0, 7)? n =1 n

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Q: 1 3 .5 4 X +x

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Q: Σ n=1 (2n+ 1)3/2 Use the Integral Test to determine if converges or diverge:

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Q: sin In(n) A) diverges B) converges 8-1

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Q: converges or diverges. I-

A: We have to find out the given series is convergent or divergent. If the series is convergent then we…

Q: Exercise 2. Determine whether the sequence of functions (fn)n converges uniformly on S. fn(x) = nx"…

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Q: 5n – 1 8) Σ 7n n=1

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Q: Show that if $a_{n}>0$ and $\Sigma a_{n}$ is convergent, then $\Sigma \ln \left(1+a_{n}\right)$…

A: Here, we are given that an > 0 and series is convergent. We need to prove that: is convergent.…

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

A: We have to show whether the series converges or diverges.

Q: CoS“ n In n а. n2 n³ n=1

A: Solution: a) ∑n=1∞cos2(n)n2+ln (n)n3

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

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Q: 3n 4. Use the ratio test to determine whether Σ converges. (n + 1)! n=1

A: use the ratio test for convergence of series.

Q: The series 1 k ln k k=2 converges. Choose an option: ()Real ()False

A: Integral Test : Suppose that f(x) is a continuous , positive and decreasing function on the interval…

Q: 5. If En-1 an converges, and if an +1 and a, > 0 for all n, (a) Show that E a converges. (b) Does E1…

A: Since, the sequence is a positive monotonically decreasing sequence, so, is also monotonically…

Q: SELECT ALI n! (2n – 1) A) converges by Divergence Test 2 B) a, = 1.3-5 ..... 2n C) diverges by…

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Q: A sequence of differentiable functions fn where fn converges uniformly and fn does not converge…

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Q: If a power series ∞ n=0 anxn converges absolutely at a pointx0, then it converges uniformly on the…

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Q: 9. Let a be a positive value. State the integral test, and use this to determine whether ). -an e…

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Q: if fn converges uniformly to f and each fn is increasing then f is increasing. Determine true of…

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Q: 3) ( series - Use the integral test to determine if the is convergent or divergent: M 1 n=7n-In(n)³

A: This is a question of series.

Q: Which test to use and is it convergent/divergent? Σ 16n2 – 8n – 3 n=1 - -

A: Use the ratio test, L=limn→∞an+1an=limn→∞116n+12-8n+1-3116n2-8n-3=limn→∞16n2-8n-316n+12-8n+1-3

Q: n²x, 0<x<1/n fm (x)== { --n²x+2n, 1/n<x<2/n ( 0, 2 n<x<I uniformly convergent on [0, 1}?

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

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Q: Exercise 2. Determine whether the sequence of functions (fn)n converges uniformly on S. 1 fn(x) = S…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

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: 9. Let a be a positive value. State the integral test, and use this to determine whether > -an e n=0…

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

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Q: 1dx x²+2x+5 -00 O diverges O None 37 converges to 4 converges to converges to converges to 3r

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Q: 5) Does vergent? (-1)"n Ln=1 \n³+2 converge absolutely, converge conditionally, or di-

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Q: n²sinx Show that g„(x) converges uniformly to x e [1,5]. 1+ n²x

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Q: 1 -dx x²+2x+5 -00 3n converges to O diverges converges to 3 4 O None converges to 4 converges to

A: Answer is 3π/8.   First option is correct one.

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: Can we use two ways to show 1 Σ n² +5n+6 n = 0 to n = infinity, convergent or divergent ? Say, 1)…

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Q: dx is convergent a) true b) false O b

A: The given integral is: ∫1∞1x2dx To find it is convergent or divergent. The integral is convergent if…

Q: nºx, 0<x<1/n fm (x)= { --n²x+2n, 1/n<x<2/n L 0, 2/n<x<1 uniformly convergent on [0, 1]?

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Q: 2sys8 y > 8 Show that Y converges in probability to a constant, and provide that constant.

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Q: 1.4 Does (fa(r)} in 1.3 converges uniformly on |-3,3]? Explain.

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