Question

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

Answer 1

cant picture the question yet the parenthesis are not clearly stated

Answer 2

as the second half of the LHS side tends to infinity hence we can neglect it
therefore the question gets reduced to
1/2x = y
now i feel if ur question is having x in numerator then answer will be
x = 2y

and if it is in denominator
then
x = 1/2y

Answer 3

\[(1/2x)+(1/2)\times(1/2x+1/2)x(1/2x)+(1/2)..... =y \]

Answer 4

This is the geometric series x/2+x/4+x/8+x/16...x/2^n=y
It follows that y/2 = x/4+x/8+x/16...+x/2^(n+1).
y-y/2=x/2-x/2^(n+1) since the intemediary terms cancel.
Also, since n tends to infinity, x/2^(n+1) tends to 0
It follows that y/2=x/2 -> x=y

Answer 5

1/2x +1/2(1/2x + 1/2(1/2x +1/2(1/2x + ... = y
If x = 1,
then the equation likes this:
1/2 +1/2(1/2 + 1/2(1/2 +1/2(1/2 + ... = y
1/2 +1/4 + 1/8 + 1/16 + 1/32 + ... = y
y = 1 = x
y = x