cho S+1/2+1/2 mũ 2+1/2 mũ 3+1/2 mũ 4+…+1/2 mũ 20. Hãy chứng tỏ rằng S<1 24/08/2021 Bởi Alice cho S+1/2+1/2 mũ 2+1/2 mũ 3+1/2 mũ 4+…+1/2 mũ 20. Hãy chứng tỏ rằng S<1
Đáp án: Giải thích các bước giải: `S = 1/2 + 1/2^2 + 1/2^3 + 1/2^4 +…+ 1/2^20 ` `1/2S=1/2(1/2+1/2^2+1/2^3+..+1/2^20)` `1/2S=1/2^2 + 1/2^3 + 1/2^4 + …+1/2^21 ` `S-1/2.S=1/2 + 1/2^2 + 1/2^3 +…+ 1/2^20 – 1/2^2 – 1/2^3 – 1/2^4 -…-1/2^21 ` ` 1/2S=1/2-1/2^21 ` ` S = ( 1/2 – 1/2^21) . 2/1` `S = 1-1/2^20 ` `S<1` Vậy `S < 1` Bình luận
`S= 1/2 + 1/2^2 + 1/2^3 + 1/2^4 +…+1/2^20` `1/2 S= 1/2(1/2 + 1/2^2 +1/2^3+…+1/2^20)` `1/2 S= 1/2^2 +1/2^3 + 1/2^4 +…+1/2^21` `S- 1/2S = 1/2 + 1/2^2 +1/2^3+…+1/2^20 – 1/2^2 – 1/2^3 – 1/2^4-…-1/2^21` `1/2 S = 1/2 – 1/2^21` `S= (1/2 – 1/2^21) : 1/2` `S= (1/2 – 1/2^21) . 2` `S= 1 – 1/2^20 <1` Vậy `S <1` Bình luận
Đáp án:
Giải thích các bước giải:
`S = 1/2 + 1/2^2 + 1/2^3 + 1/2^4 +…+ 1/2^20 `
`1/2S=1/2(1/2+1/2^2+1/2^3+..+1/2^20)`
`1/2S=1/2^2 + 1/2^3 + 1/2^4 + …+1/2^21 `
`S-1/2.S=1/2 + 1/2^2 + 1/2^3 +…+ 1/2^20 – 1/2^2 – 1/2^3 – 1/2^4 -…-1/2^21 `
` 1/2S=1/2-1/2^21 `
` S = ( 1/2 – 1/2^21) . 2/1`
`S = 1-1/2^20 `
`S<1`
Vậy `S < 1`
`S= 1/2 + 1/2^2 + 1/2^3 + 1/2^4 +…+1/2^20`
`1/2 S= 1/2(1/2 + 1/2^2 +1/2^3+…+1/2^20)`
`1/2 S= 1/2^2 +1/2^3 + 1/2^4 +…+1/2^21`
`S- 1/2S = 1/2 + 1/2^2 +1/2^3+…+1/2^20 – 1/2^2 – 1/2^3 – 1/2^4-…-1/2^21`
`1/2 S = 1/2 – 1/2^21`
`S= (1/2 – 1/2^21) : 1/2`
`S= (1/2 – 1/2^21) . 2`
`S= 1 – 1/2^20 <1`
Vậy `S <1`