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Question

anonymous · Answer

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

hartnn · Answer

you can replace the identical infinite series within that series by y 
 1/2x +1/2(1/2x + 1/2(1/2x +1/2(1/2x + ... = y, 

 1/2x +1/2($ \large 1/2x + 1/2(1/2x +1/2(1/2x + ...)$ = y, 
 1/2x +1/2$(y)$ = y, 

now can u solve this for y ?

hartnn · Answer

u see what i did there ?

anonymous · Answer

yes but can i do it like this: @hartnn 
1/2x +1/2(1/2x + 1/2(1/2x +1/2(1/2x + ... = y 
If x = 1, 
then the equation is like 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

hartnn · Answer

that gives the correct answer but the approach is not good, you can't just let x=1 ...

anonymous · Answer

ok i see thank you @hartnn

hartnn · Answer

also, x=y is true for any value of x, you verified it for x=1.
welcome ^_^