E. i. Suppose that the sn satisfies both limn→∞ s2n = 3 and limn→∞ s2n+1 = 3. (That is, the sequence given by the even terms of sn and that given by the odd terms of sn both converge to 3.) Show that also limn→∞ sn = 3. ii. Give an example of a sequence where the sequences given by the even and by the odd terms both converge, but where the entire sequence does not converge.

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Q: i. Suppose that the sn satisfies both limn→∞ s2n = 3 and limn→∞ s2n+1 = 3. (That is, the sequence…

A: Given: Sequence sn such that limn→∞s2n=3 and limn→∞s2n+1=3.To show:(i) limn→∞sn=3 (ii) Find An…

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Q: uppose that the sn satisfies both limn→∞ s2n = 3 and limn→∞ s2n+1 = 3. (That is, the sequence given…

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Q: i. Suppose that the sn satisfies both limn→∞ s2n = 3 and limn→∞ s2n+1 = 3. (That is, the sequence…

A: (i) Given :A sequence sn satisfies both limn→∞s2n=3  and  limn→∞s2n+1=3. To show: limn→∞sn=3. (ii)…

Q: advanced MATH   Suppose that the sn satisfies both limn→∞ s2n = 3 and limn→∞ s2n+1 = 3. (That is,…

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Q: i. Suppose that the sn satisfies both limn→∞s2n = 3 and limn→∞s2n+1 = 3. (That is, the sequence…

A: (i) Suppose a given a sequence sn. Even terms of the sequence converges to 3. that is, limn→∞s2n=3…

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A: A sequence represented by say bn; if converges thenlimn→∞bn=0. It is important to note that the…