If ∑x_n and ∑y_n are convergent, show that ∑(x_n + y_n) is convergent.

Q: every convergent cauchy Show that Sequence is but the converse is not true general. in

A: Let, be the convergent sequence which converges to . Since, then, for the given ,

Q: Wi n=1 (-2)^ n! n^

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Q: A bag contains 3 red marbles, three green ones, 1 lavender one, two yellows, and 4 orange marbles.…

A: We have to find number of possible sets of three marbles using given data Formula required:  Number…

Q: ∑(sqrt(n+1) - sqrt(n))/sqrt(n2+n) does it converge or diverge? (show each step please)

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Q: Show that sum of two uniformly convergent sequen ce is uniformly convergent

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Q: Petomim whemer mi sunes conmerges If it hnd ti r Conver dhverget. um. -n-2 n² + Tn 12 n=1

A: Check whether the series ∑n=1∞6n2+7n+12+4-n-22n converges or not. If it is convergent, then find the…

Q: Use the root test to determine whether convergent or divergent from k=1 and ♾ of (9k+2/16k+1)^-k/2

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Q: 1. (x² + 1)² dr

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Q: Can you further solve how exactly to find a convergent subsequence here?

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Q: find if it converges ∑∞ n=0((4n)!(1103+26390n))/(3964n (n!))  (show each step please)

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Q: Converges (by the Limit Comparison Test)

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Q: Examine the convergence of the sequence an=sin2n/2n whose general term is (an) Find the limit with…

A: Given sequence is an=sin2n2n. We have to check convergence of the given sequence and then find the…

Q: Let {an} be a monotonic sequence such that an ≤ 1. Discuss the convergence of {an}. When {an}…

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

A: Solution

Q: ind the limit if the attached sequence converge

A: Given :an=cos2n2n

Q: compute the 9-th convergent to √29.

A: We need to find the smallest positive integer solution to  or compute the  convergent to .We will…

Q: is convergent to

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Q: 2) is E=1 2n convergent?

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

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Q: check if the fixed point itteration converge or diverge for  (x^3/3)+4 in interval [4,5]

A: f(x) = (x^3/3)+4

Q: Suppose that f is a bounded non-negative measurable function. Show that there exists a decreasing…

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Q: If xi 2, 3dn-1+ 3"n-2 show that {xn} is convergent. identify the limit.

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Q: 4n2 Determine if the sequence {an}I with an= converges. If it converges write its limite if it…

A: Given Data The sequence formula an is:     The expression for the limit of sequence an is,

Q: Prove that ∑^infinity_(n=1) ((-1)^n/n) converges.

A: Apply Ditichlet theorem.