The Problem With Infinity

Infinities don't behave like proper numbers. It makes sense to write  
\[x--x=0\]
  when  
\[x\]
  is an ordinary number but not when  
\[x\]
  is infinity. This is because when  
\[x\]
  is multiplied by 2 the result is  
\[2x\]
  but when infinity is infinity is multiplied by infinity, the result is infinity.
Because of this following proof contains an error.
\[S=1++2+4+8+16+32+...+ \infty +...\]
(1)
\[2S=2+4+8+16+32+...+ \infty +...\]
(2)
(2)-(1) gives
\[S=-1\]
. This is obviously wring since all terms rare positive. The above technique will only work if  
\[\frac{a_{n+1}}{a_n} =r  for  
\[n=1,2,3,...\]