1. The problem statement, all variables and given/known data
A bored student enters the number 0.5 in her calculator, then repeatedly computes the square of the number in the display. Taking A0 = 0.5, find a formula for the general term of the sequence {An} of the numbers that appear in the display, and find the limit of the sequence {An}.
2. Relevant equations
3. The attempt at a solution
So, I'm having a difficult time finding a standard rule to this sequence. The only thing I came up with was an= (a(n-1))2. Then it doesn't seem reasonable to show the limit of this sequence is = 0 as n increases, an decreases. Is there another way of finding a rule that is easier to work with?
A bored student enters the number 0.5 in her calculator, then repeatedly computes the square of the number in the display. Taking A0 = 0.5, find a formula for the general term of the sequence {An} of the numbers that appear in the display, and find the limit of the sequence {An}.
2. Relevant equations
3. The attempt at a solution
So, I'm having a difficult time finding a standard rule to this sequence. The only thing I came up with was an= (a(n-1))2. Then it doesn't seem reasonable to show the limit of this sequence is = 0 as n increases, an decreases. Is there another way of finding a rule that is easier to work with?
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