Question

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

Answer 1

is the x in the denominator or numerator. Is it
\[ \frac{1}{2x} or \frac{1}{2}x ?\]

Answer 2

Let's assume it is (1/2)x = \( \frac{1}{2} x \)
Notice you can rewrite the sum as
\[ y= \frac{1}{2}x + \frac{1}{4}x + \frac{1}{8}x + ... \]
or
\[ y= x(\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ... )\]
Call the sum in the parentheses S:
\[ S=\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ... \] and
\[ \frac{1}{2}S=\frac{1}{4} + \frac{1}{8} + ... \]
subrtract the two series to get
\[ \frac{1}{2}S= \frac{1}{2} \]
or S=1
so we find
\[ y=x \]