S= 7/2 + 7/ mũ 2+ 7/2 mũ 3 +…+ 7/2 mũ 20 cần gấp 17/11/2021 Bởi Lydia S= 7/2 + 7/ mũ 2+ 7/2 mũ 3 +…+ 7/2 mũ 20 cần gấp
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} ` Bình luận
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} `
Bạn tham khảo :