ENERGEL Needle Tip 0.5 mm ball Give an example of two divergent sequences {x} and {y} = such that... C a.) { xn³. - {yn=1 converges where b.) Exn ynn, converges where Xn xn #yn Xn #yn \nEN Xn # / VEN Yn

Q: E(-1)". 9 + In n n=1 Input C for convergence and D for divergence:

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Q: What are all of the values of x ,such that E-1)n+1(n)* converges? x1.2 O x<1.30 x<0,40

A: By lebnitz test we observe n^x tends to inf gives zero only when x&lt;0.

Q: Which of the following information is correct for the sequence 4 dx 6. dx 8. 1 r dx dx - n31 8. 6. 1…

A: We will find the limit

Q: (n²)(1 - cos(뉴)). 1.5 COS An

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Q: (ann-1 converges, but 32. Find the limit of the sequences with general term as given: n² + 4n (a) n²…

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Q: converge Hw Deternineif the fallowing serief -2n n31

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Q: lim s n where s₁ = 1, and S n+1 = (1 – = -)Sn n+31 for n ≥ 1.

A: We first evaluate the first few values of the sequence

Q: O4l determine if the geometric series converges o diverges o If seri es converg es, find its sum 3.…

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Q: Sequences {xn} and {yn} such that they are both convergent and {xn+yn} maps to 5

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Q: Let X = C[0,4], with the usual notation and suppose X is endowed with the norm, ||f||2 Consider the…

A: Let X=C0, 4, with the usual notation and suppose X is endowed with the norm,…

Q: Show that the sequence f.(x)} converges to a limit function (that you should determine) for each XEI…

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Q: Prove that if {an} is a bounded sequence (not necessarily convergent) and {bn} converges to 0, then…

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Q: Please no written by hand and no emage Let {Dm} be a non-increasing sequence of events. Verify that…

A: Here, the sequence  { Dn} is monotonous non- decreasing or expanding sequence of events. In this…

Q: Let {xn} be a bounded sequence on R. Show that lim n-+o N = 0.

A: Given that {xn} be a bounded sequence on ℝ.So,           a≤ xn≤ b,   where a and b are any…

Q: using agraph comparison te ot explain continouw on T0,00) and lim fead=l, Is it 2900 possible theu…

A: We can evaluate an exact value of a definite integral. But, for improper integral, we can't evaluate…

Q: ап +1 anx" Suppose that + 1 as n → . Find the radius of convergence. An 4" n=1

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Q: o prove thab lie n VA =| Test the Sequence CconVeordiv) an = (^-!) 15 an= 3ntl 3n-1 an=

A: A sequence is said to be convergent if it approaches some limit

Q: g) an = In(n+ 1) – In(n) (Hint: simplify the logarithms) (-3)" h) an n! i) an = Vn + 2 – V2n

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Q: (In(n))" 00 Find the value(s) of a such that 2 is convergent T2 Answer:

A: Given that, ∑n=2∞lnnan By using the integral test, ∫2∞lnnandn It can be written as, ∫2∞1nlnnadn

Q: Determine the limit of the following convergent sequence: { 2020 4+(-0.1)" nEN Which one of the…

A: We see that, The limit as n tends to infinity, f(n) = 2020/[4+(-0.1)^n], is [2020/(4+0)] = 2020/4 =…

Q: If xi > 0 and xn+1 := (2+ xn)¯' for n> 1, show that (x,„) is a contractive sequence. Find the limit.

A: We only solve one problem at a time so please submit the next question separately which you want to…

Q: Let (Xn} be a sequence of rv's such that X, is distributed as Z with probability pn and as onZ with…

A: The central limit theorem (CLT) is one of the most important results in probability theory. It…

Q: does the sequence an converge or diverge? Find the limit if the sequence is convergent…

A: givenan=cos(3pi2 - 6n)

Q: H.w, Determine whether Ithe lollowing functions Convergent or divergent sequenee of (fa) = Sin (nx…

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Q: 00 (2х+3)" 2 2n+n-1 n=1

A: Given series is ∑n=1∞(2x+3)n2n2+n-1