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

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

A: givenan=cos(3pi2 - 6n)