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find the limit of the sequence

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A bored student enters the number 0.5 in her calculator, and then repeatedly computes the square of the number in the display. Taking a_0 = 0.5, find a formula for the general term of the sequence {a_n} of the numbers that appear in the display, and find the limit of the sequence {a_n}.

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In this solution, we explain how to determine the limit of the given sequence.

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