Đáp án + giải thích bước giải :
`A = 2 + 2^2 + ... + 2^{10}`
`-> 2A = 2^2 + 2^3 + ... + 2^{11}`
`-> 2A - A = (2^2 + 2^3 + .... + 2^{11}) - (2 + 2^2 + ... + 2^{10})`
`-> A = 2^{11} - 2`
`-> A = 2046`
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`B = 1/(1 . 2) + 1/(2 . 3) + ... + 1/(9 . 10)`
`-> B = 1 - 1/2 + 1/2 - 1/3 + .... + 1/9 - 1/10`
`-> B = 1 + (- 1/2 + 1/2 - 1/3 + .... + 1/9) - 1/10`
`-> B = 1 - 1/10`
`-> B = 10/10 - 1/10 = 9/10`
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Ta có :
`2046 = (2046 . 10)/(1 . 10) = 20460/10`
`9/10`
`-> 20460/10 > 9/10`
hay `2046 > 9/10`
`-> A > B`
