Mathematics 84 Online
OpenStudy (anonymous):

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

OpenStudy (anonymous):

cant picture the question yet the parenthesis are not clearly stated

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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