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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