Question

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

Answer 1

$y=\dfrac{1}{2}x+\dfrac{1}{2}\left(\dfrac{1}{2}x+\dfrac{1}{2}\left(\dfrac{1}{2}x+\ldots \Longleftrightarrow y=\dfrac{1}{2}x+\dfrac{1}{2}y$

$y=\dfrac{1}{2}x+\dfrac{1}{2}y\\\\ 2y=x+y\\\\ \boxed{x=y}$