Question: (3) Let (r, ), be a given sequence and r be a given real number. Suppose that (In) does not converge to r. Show that

(3) Let (r, ), be a given sequence and r be a given real number. Suppose that (In) does not converge to r. Show that there exist a positive number a > 0 and a subsequence (T, ) of (1,)=1 such that In - | > o for any k E N. (Hint: the proof of this fact is embedded in a proof of another result in the lecture.)

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