Ta có:
` S = 7/2 + 7/2^2 + 7/2^3 + ... + 7/2^{20} `
` <=> 2/7 S = 1 + 7/2 + 7/2^2 + ... + 7/2^{19} `
` <=> 2/7 S - S = 1 + 7/2 + 7/2^2 + ... + 7/2^{19} - 7/2 - 7/2^2 - 7/2^3 - ... - 7/2^{20} `
` <=> -5/7 S = 1 + (7/2 - 7/2) + (7/2^2 - 7/2^2) + ... + (7/2^{19} - 7/2^{19}) - 7/2^{20} `
` <=> -5/7 S = 1 - 7/2^{20} `
` <=> S = (1 - 7/2^{20}) : \frac{-5}{7} `
` <=> S = \frac{-7}{5} - \frac{-49}{5.2^{20} `
Vậy ` S = \frac{-7}{5} - \frac{-49}{5.2^{20} `
