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

Q: Prove that the sequence {cn} converges to c if and only if the sequence {cn- c} converges to 0.

A: To prove that the relation between the limits of the two given sequences

Q: For the sequence { 4^(-n) } a) determine whether or not is convergent b) if it is convergent,…

A: The nth term of the given sequence is given by bn=4-n. If limn→∞bn exists, the sequence bn is…

Q: Find the limit of the sequence whose nth term is an = In(2n + 1) or show the sequence diverges. Be…

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Q: [n^2cos(n/2)] / 2n^2 +1 does this sequence converge or diverge & w

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Q: What is the probability that given a block n of 30 bits, that you have an error sequence E(X)=P(X)…

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Q: Show that the sequence defined by 1 a₁ = 1 an is increasing and an < 3 for all n. Deduce that {an}…

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

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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: Converges (by the Limit Comparison Test)

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Q: {   x_(n+1) = 3 + [6/(3 + x_n)]     } Beginning with a firs approximation of x_1 = 4, find the next…

A: This is a problem of Sequence.

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: ind the limit if the attached sequence converge

A: Given :an=cos2n2n

Q: A sequence U_(n) is defined by {(7n)/(2n-1)}. List the first five elements of U_(n).

A: The answer is in step 2.

Q: Determine if the sequences converge or diverge.  an = (ln n)/ln 2n   an = e^-n ln n   an = (3n…

A: • Sequence 1: Inconclusive • Sequence 2: Converges (e^-n dominates) • Sequence 3: Converges…

Q: Evaluate an improper intergral. determine whether its convergent or divergent. 2 through infinity…

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Q: Prove that sequence {an}= {(-1)n} does not have a limit.

A: According to the given information it is required to show that {an}= {(-1)n} has no limit.

Q: (a) (1+n)-2

A: According to our terms and conditions I have solved first part for next parts repost

Q: Use limit comparison test for sum of n=1 to ♾ of (3n^3+2)^(1/2)/(8n^2+9n+1)

A: take bn = 1/n  we know that if limn→∞anbn= finite  then by limit comparison test both series behave…

Q: determine whether the sequence converges or diverges.if it converged find its limit.…

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Q: Find a sequence of real numbers {a;} such that lim a, does not n-00 xist, but it has 3 subsequential…

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Q: Use Squeeze Theorem to find the limit of the sequence {4n/n!}

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Q: [ (7)^ 걔 V (x+5) ^

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Q: Only use epsilon defination , Let be a sequence of positive terms such that pn-> p show that…

A: We apply only Epsilone defination.

Q: Let (In) = 1, be sequence in R, dis usual metric %3D then (an) is Cauchy sequence True O False

A: Cauchy sequence

Q: Write the first 5 terms of the sequences with general terms an below and indicate whether they are…

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Q: Is it true that a sequence {an} of positive numbers must converge if it is bounded from above? Give…

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Q: Explain the the convergence of functions as an example of discrete math functions

A: We find the z transforms for the following functions and indicate the region of convergence for each…