# Can somebody explain this logic to me If S=1+3+9+27... Isn't 3S=3+9+27+81... Then wouldn't 3S-S=(3+9+27+81...)-(1+3+9+27...) 2S=-1+(3-3)+(9-9)+(27-27)+(81-81)... 2S=-1 So, isn't the entire series just-1/2? What is wrong with the "proof"?