an Show that if lim bn =0 and =1 n- 00 converges then En=1ªn converges too. n=D1

Q: If lim M dx converges, then which of the xP following must be true? Select one: 1 a. converges. n=1…

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Q: If an converges and > 0 for all n , can anything be said about E–? An an

A: Given that, ∑ an  converges We known that, the series if  ∑n = 1∞ an  is convergent then limn→∞ an =…

Q: M dx converges, then which of the If lim xP following must be true? Select one: 1 converges. а. NP-2…

A: The correct option is given below.

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: Determine whether the given converges or diverges. n Σ 2n + 1 n=1

A: Given is a series ∑n=1∞n2n+1n To check if the given series is convergent or divergent Ratio test:…

Q: Suppose that a, > 0 and b, > 0 for n > N (N an integer). If lim, 00 1,¬- (an/bn) = ∞ and Sa,…

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Q: a) Determine if Eº, absolutely converges, conditionally converges, or diverges. ´n=2 n-yn

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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: 5. Find all values of x >0 so that ) converges. 3k k=2

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Q: 00 Fn+1 { is convergent, and Show that the sequence Fn n=1 1 Fn+1 lim n→∞ Fn Fn+1 > 1 and Fn-1…

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Q: whether the sequence an = 1+ converges and, if it does, find the limit. ) diverges 3 O converges to…

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Q: (-1)ªn n² + 1 mula converges to a value or diverges withou

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Q: 2 then E " Cn+1 converges. 3.11 limnr+m

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Q: 7N 8N 3) Show that converges/diverges.

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Q: Show that > iP converges to a finite value iff p < –1. i=1

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

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Q: ‘?

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Q: an If lim Σ =0 and En=1"n converges, then bn 'n=1 b, diverges.? n+ o0 True O False

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

A: We can solve this as follows:

Q: Suppose that the sn satisfies both limn→∞ s2n = 2 and limn→∞ s2n+1 = 2. (That is, the sequence given…

A: Step:-1 Limit of a sequence:- Let f(n) be a sequence of real numbers and let l be a real number then…

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

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Q: If 0< by <1 for all k and , br converges, then , converges. Lk-1 %3D1 Select one: True O b. None of…

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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: 5. (a) Suppose 1 and Xn+1 = 2 Show that {n} converges and find the limit. X1 for all nEN.

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

A: Series convergence test problem.....

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

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

Q: 22n Σ n! n=1

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Q: find if diverges or converges. if converges, then find its limit cos²(8n) An 8n-1

A: Given - an = cos28n8n - 1 To find - find if diverges or converges. If converges, then find its…

Q: .8.8 Suppose that Cn >0 for each n E N. Prove that n either converges = diverges to infinity.

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Q: converges for all * > 0 because lim a - In n 0, for all * > 0- n=2 True False

A: Need to check given statement is true or false.

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: ,(-1)" converges conditionally, but not absolutely. Show all work. 3n Prove E

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

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

Q: 1 x converges 1 ex - e-X Select one: True False

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Q: If fn If 0 ≤ an ≤ bn for all n € N, and f on [a, b], then lim ſå fn ‡ få f. an converges, then bn…

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Q: If > an converges, then a converges. n=1 n=1

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

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Q: n· 3n 5n n=

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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) Find all values of x for which En=1 nxn (n+1)(2x+1)n converges absolutely.

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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: O Does Eo 2k+² e-k converge or diverge? If it converges find the sum. "k=1'

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Q: 1 Show that the series 2 converges. k=2 k(log k)?

A: Given: ∑k=2∞1klogk2

Q: the series : 2 3 3 5 Select one: a. converges absolutely O b. converges conditionally c. diverges d.…

A: Check the given series by limit comparision test.

Q: 2" Зп+2 n=0

A: