If 1/2x +1/2(1/2x + 1/2(1/2x +1/2(1/2x + ... = y, then x = ?

If 1/2x +1/2(1/2x + 1/2(1/2x +1/2(1/2x + ... = y, then x = ?
in Algebra 2 Answers by Level 1 User (120 points)

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2 Answers

(1/2) + (1/4) +(1/8) +(1/16) +...=1 . . . multipli bi x & yu get x
by
"Solution:
Given 1/2x +1/2(1/2x + 1/2(1/2x +1/2(1/2x + ... = y x = y
Taking 5 iterations:
y =.5x + .5(.5x + .5(.5x + .5(.5x + .5(.5x))))
y = .5x + .5(.5x +.5(.5x + .5(.5x + .25x)))
y = .5x + .5(.5x + .5(.5x + .5(.75x)))
.75x is the result of 2 iterations
y = .5x +.5(.5x + .5(.5x + .375x))
y = .5x + .5(.5x + .5(.875x))
.875x is the result of 3 iterations
y = .5x + .5(.5x +.4375x)
y = .5x + .5(.9375x) .9375x is theresult of 4 iterations
y = .5x + .46875x
y = .96875x .96875x is the result of 5 iterations
the number of
iterations approaches infinity, x approaches y. "
by Level 4 User (5.6k points)

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