: If 1/2x +1/2(1/2x + 1/2(1/2x +1/2(1/2x + ... = y, then x = ?
cant picture the question yet the parenthesis are not clearly stated
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
\[(1/2x)+(1/2)\times(1/2x+1/2)x(1/2x)+(1/2)..... =y \]
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
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
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