` S = 1/2 + 1/2^2 +1/2^3 + ... +1/2^20`
` 2S = 1 + 1/2 + 1/2^2 + ... +1/2^19`
` \to 2S - S = ( 1 + 1/2 + 1/2^2 + ... +1/2^19) - (1/2 + 1/2^2 +1/2^3 + ... +1/2^20)`
` \to S = 1 + 1/2 + 1/2^2 + ... +1/2^19 - 1/2 - 1/2^2 -1/2^3 - ... - 1/2^20`
` \to S = 1 - 1/2^20 < 1` (đpcm)