Use Theorem 3 to show that the sequence 0.7, 0.77, 0.777, 0.7777, 0.77777, 0.777777, 0.7777777, ... has a limit.

Theorem 3 is ...

Suppose that the sequence is nondecresing and bounded above by a number A. That is,

Then converges to some finite limit a, with a . Similarly, if is nonincreasing and bounded below by a number B, then converges to a finite limit .

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