1. Recall the definition of the limit of a sequence of real numbers (xn) = (x1, X2, X3, . . .) "(Tn) converges to L' means: Ve > 0, 3N e N such that n > N =| xn – L |< € State what it means for a sequence (xn) not to converge to L.

Q: (f) Assume that g(x) > bna" is convergent on (-R, R). Instead of assuming that f(rn) = 0 assume that…

A: We will prove the part (f) using two theorems   Theorem (a)Let f(x)=∑anxn be a non-constant power…

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A: see my solution

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A: This question is basically based on the theorem named Banach fixed point Theorem which states that:…

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A: a: The sequence is xk=1/ke1-k-2/k2. At k = 1, x1=11-2; at k = 2, x2=1/2e-1-1/2; at k = 3,…

Q: 8. (a) Give an example of a convergent sequence (s) of positive numbers such that lim (s/s) 1. (b)…

A: (Sn​)=(1+n1​) (tn​)=(n)Explanation:

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Q: 1.) Prove that the sequence An= nt n In (2+1) converges to O. That is, prove limln (^+1)=0 nyo

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Q: (b) Prove that lim,→20,¤€A ƒ (x) exists and is equal to lim→0 Yk-

A: This problem is related to the sequence of functions. Given:  fkk∈ℕ is a sequence of functions from…

Q: Write out the first five terms of the sequence with, [(1 - 7)", determine whether the sequence…

A: To write out the first five terms of the sequence with 1-7n+7nn=1∞, to determine whether the…

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A: There are multiple question. As per company policy kindly ask other question separately. a. This…

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A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three sub…

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A: As per our guidelines we are suppose to answer only 3 sub-parts.

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A: Given sequences: (a): (b): (c): (d): where  and  satisfy We have to find the limit of the given…

Q: 4. Consider the sequence a- (). n2 1, k>0. An kn – 2 (a) Determine the values of k for which the…

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