{ [1/3+1/4]x1 và 1/3+2/9}:0,8-1/4+2021
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a: =(-1)+(-1)+...+(-1)=-1011
b: =(-5)+(-5)+...+(-5)=-175
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B/A
\(=\dfrac{1+\dfrac{2020}{2}+1+\dfrac{2019}{3}+...+1+\dfrac{1}{2021}+1}{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2021}+\dfrac{1}{2022}}\)
\(=\dfrac{2022\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2021}+\dfrac{1}{2022}\right)}{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2021}+\dfrac{1}{2022}}=2022\)
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B = \(\dfrac{1}{2002}\) + \(\dfrac{2}{2021}\) + \(\dfrac{3}{2020}\)+...+ \(\dfrac{2021}{2}\) + \(\dfrac{2022}{1}\)
B = \(\dfrac{1}{2002}\) + \(\dfrac{2}{2021}\) + \(\dfrac{3}{2020}\)+...+ \(\dfrac{2021}{2}\) + 2022
B = 1 + ( 1 + \(\dfrac{1}{2022}\)) + ( 1 + \(\dfrac{2}{2021}\)) + \(\left(1+\dfrac{3}{2020}\right)\)+ ... + \(\left(1+\dfrac{2021}{2}\right)\)
B = \(\dfrac{2023}{2023}\) + \(\dfrac{2023}{2022}\) + \(\dfrac{2023}{2021}\) + \(\dfrac{2023}{2020}\) + ...+ \(\dfrac{2023}{2}\)
B = 2023 \(\times\) ( \(\dfrac{1}{2023}\) + \(\dfrac{1}{2022}\) + \(\dfrac{1}{2021}\) + \(\dfrac{1}{2020}\)+ ... + \(\dfrac{1}{2}\))
Vậy B > C
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\(0,8.\sqrt{\frac{25}{9}}-\frac{2}{7}.\sqrt{5}.\frac{4}{9}+\left(-\frac{1}{2}\right)^3.4^2\)
\(=\frac{4}{3}-0,29+\left(-2\right)\)
\(=\frac{313}{300}+\left(-2\right)\)
\(=-\frac{287}{300}\)
P/s : kh chắc nhé
\(0,8.\sqrt{\frac{25}{9}}-\frac{2}{7}.\sqrt{5}.\frac{4}{9}+\left(\frac{-1}{2}\right)^3.4^2\)
\(=0,8.\frac{5}{3}-\frac{2}{7}.\frac{11}{2}.\frac{4}{9}+\frac{-1}{8}\)
\(=\frac{4}{3}-\frac{44}{63}+\frac{-1}{8}\)
\(=\frac{-1}{8}\)
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a) Ta có:
2A=2.(12+122+123+...+122020+122021)2�=2.12+122+123+...+122 020+122 021
2A=1+12+122+123+...+122019+1220202�=1+12+122+123+...+122 019+122 020
Suy ra: 2A−A=(1+12+122+123+...+122019+122020)2�−�=1+12+122+123+...+122 019+122 020
−(12+122+123+...+122020+122021)−12+122+123+...+122 020+122 021
Do đó A=1−122021<1�=1−122021<1.
Lại có B=13+14+15+1360=20+15+12+1360=6060=1�=13+14+15+1360=20+15+12+1360=6060=1.
Vậy A < B.
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`[(1/3+1/4) xx 1 1/3 + 2/9 ] : 0,8 - 1/4 + 2021`
`= [(4/12+3/12) xx 4/3 +2/9] :4/5 - 1/4+2021`
`= [7/12 xx 4/3+2/9]:4/5 - 1/4+2021`
`=[7/9+2/9):4/5-1/4+2021`
`=1 :4/5-1/4+2021`
`=1 xx 5/4 -1/4+2021`
`=5/4-1/4+2021`
`=1+2021`
`=2022`