Đáp án:
`S = 1/2 + 1/2^2 + 1/2^3 + ... + 1/2^{2018} + 1/2^{2019}`
`text{Từ tổng trên}`
`-> S > 1/2 (1)`
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`S = 1/2 + 1/2^2 + 1/2^3 + ... + 1/2^{2018} + 1/2^{2019}`
`-> 1/2S = 1/2^2 + 1/2^3 + 1/2^4 + ... + 1/2^{2019} + 1/2^{2020}`
`-> S - 1/2S = ( 1/2 + 1/2^2 + 1/2^3 + ... + 1/2^{2018} + 1/2^{2019}) - (1/2^2 + 1/2^3 + 1/2^4 + ... + 1/2^{2019} + 1/2^{2020})`
`-> 1/2S = 1/2 - 1/2^{2020}`
`-> S=(1/2 - 1/2^{2020}) ÷ 1/2`
`-> S = 1/2 × 2 - 1/2^{2020} ×2`
`-> S = 1 - 1/2^{2019}`
`text{Ta thấy :}` `1- 1/2^{2019} < 1`
`-> S < 1 (2)`
$\\$
`text{Từ (1) và (2)}`
`-> 1/2 < S < 1`
