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}
work shown:
the series is a geometric series with a=1/2 and r=1/2
therefore the sigma notation from (n=1 to infinity) of 1/(2^n) = 1
therefore the sum is equal to 1...
and the limit of 1/(2^n) as n goes from 1 to inf. is equal to zero
I'm not sure if my approach and work is correct here please help me with this equation
work shown:
the series is a geometric series with a=1/2 and r=1/2
therefore the sigma notation from (n=1 to infinity) of 1/(2^n) = 1
therefore the sum is equal to 1...
and the limit of 1/(2^n) as n goes from 1 to inf. is equal to zero
I'm not sure if my approach and work is correct here please help me with this equation