So sánh
A = 2 + 2^2 + … + 2^10
với B = 1/(1 . 2) + 1/(2 . 3) + … + 1/(9 . 10)
So sánh A = 2 + 2^2 + … + 2^10 với B = 1/(1 . 2) + 1/(2 . 3) + … + 1/(9 . 10)
By Anna
By Anna
So sánh
A = 2 + 2^2 + … + 2^10
với B = 1/(1 . 2) + 1/(2 . 3) + … + 1/(9 . 10)
`A=2+2^2+2^3+…+2^10`
`2A=2^2+2^3+2^4+…+2^11`
`2A-A=(2^2+2^3+2^4+…+2^11)-(2+2^2+2^3+…+2^10)`
`A=2^11-2`
`A=2048-2=2046`
`B=1/(1 . 2) + 1/(2 . 3) + … + 1/(9 . 10)`
`B=1/1-1/2+1/2-1/3+…+1/9-1/10`
`B=1/1-1/10=10/10-1/10=9/10`
Ta có: `2046=2046/1={2046.10}/{1.10}=20460/10>9/10`
`=>2046>9/10`
`=>A>B`
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`