\(2019+2.2018+2^2.2017+2^3.2016+...+2^{2019}.1< 2^{2020}\)

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28 tháng 3 2021

ta có :\(E=\frac{2019^{2019}+1}{2019^{2020}+1}\Leftrightarrow2019\cdot E=\frac{2019^{2020}+2019}{2019^{2020}+1}=1+\frac{2019}{2019^{2020}+1}\)

\(F=\frac{2019^{2020}+1}{2019^{2021}+1}\Leftrightarrow2019\cdot F=\frac{2019^{2021}+2019}{2019^{2021}+1}=1+\frac{2019}{2019^{2021}+1}\)

vì \(\frac{2019}{2019^{2020}+1}>\frac{2019}{2019^{2021}+1}\) nên E>F

28 tháng 3 2021

E=2019 x 2019 x 2019 x ........ x 2019 x2019 +1 /2019 x 2019 x 2019 x.........x 2019 x 2019 + 1

E=1+1/2019+1

E=2/2020

E=1/1010

F=2019 x 2019 x 2019 x .......... x 2019 x 2019 +1 / 2019 x 2019 x 2019 x ....... x 2019 x 2019 +1

F= 1+1/2019+1

F=2/2020

F=1/1010

từ đó ta có E=F(=1/1010)

5 tháng 3 2020

\(4S=1+\frac{2}{4}+\frac{3}{4^2}+...+\frac{2019}{4^{2018}}\)

=> \(3S=1+\frac{2}{4}+\frac{3}{4^2}+...+\frac{2019}{2^{2018}}-\frac{1}{4}-\frac{2}{4^2}-\frac{3}{4^3}-...-\frac{2019}{4^{2019}}\)

=>3S=\(1+\frac{1}{4}+\frac{1}{4^2}+..+\frac{1}{2^{2018}}-\frac{2019}{4^{2019}}\)

còn lại tự giải nhé  

5 tháng 3 2020

Mình cảm ơn bạn.

\(A=\frac{2019^{2020}+1}{2019^{2021}+1}\)và \(B=\frac{2019^{2018}+1}{2019^{2019}+1}\)

Xét \(A=\frac{2019^{2020}+1}{2019^{2021}+1}\Rightarrow2019A=\frac{2019^{2021}+2019}{2019^{2021}+1}=1+\frac{2019}{2019^{2021}+1}\)

Xét \(B=\frac{2019^{2018}+1}{2019^{2019}+1}\Rightarrow2019B=\frac{2019^{2019}+2019}{2019^{2019}+1}=1+\frac{2018}{2019^{2019}+1}\)

Vì \(1+\frac{2018}{2019^{2021}+1}< 1+\frac{2018}{2019^{2019}+1}\Rightarrow\frac{2019^{2020}+1}{2019^{2021}+1}< \frac{2018^{2019}+1}{2019^{2019}+1}\)

\(\Rightarrow A< B\)

Ta có:

\(A=\frac{2019^{2020}+1}{2019^{2021}+1}\)

\(\Rightarrow2019A=\frac{2019^{2021}+2019}{2019^{2021}+1}\)

\(\Rightarrow2019A=1+\frac{2019}{2019^{2021}+1}\)

\(\Rightarrow A=1+\frac{2019}{2019^{2021}+1}:2019\)

Ta lại có:

\(B=\frac{2019^{2018}+1}{2019^{2019}+1}\)

\(\Rightarrow2019B=\frac{2019^{2019}+2019}{2019^{2019}+1}\)

\(\Rightarrow2019B=1+\frac{2019}{2019^{2019}+1}\)

\(\Rightarrow B=1+\frac{2019}{2019^{2019}+1}:2019\)

Do \(2019^{2021}+1>2019^{2019}+1\)

\(\Rightarrow\frac{2019}{2019^{2021}+1}< \frac{2019}{2019^{2019}+1}\)

\(\Rightarrow1+\frac{2019}{2019^{2021}+1}:2019< 1+\frac{2019}{2019^{2019}+1}:2019\)

\(\Rightarrow A< B\)

Vậy \(A< B.\)

7 tháng 7 2017

\(2\cdot\left(2x-6\right)+\left(x-1\right)=2\)

\(\Leftrightarrow4x-12+x-1-2=0\)

\(\Leftrightarrow5x-15=0\)

\(\Leftrightarrow5x=15\)

\(\Leftrightarrow x=3\)

25 tháng 8 2017

\(2^4.2^9=2^{4+9}=2^{13}\)

25 tháng 8 2017

24.29=24+9=213

21 tháng 3 2020

ta có : 3.\(|2x^2-7|\)= 33

nên \(|2x^2-7|\) =33:3

=>2x-7=11 (vì -5<x<10 và \(x^2\ge0\) )

=>2x2=11+7

=>2x2 =18

=>x2 =9

=>x=3 hoặc x=-3

Vậy .......

21 tháng 3 2020

3./2x^2 -7/ =33

/2x^2-7/= 11

Ta có x^2 >=0 và 7 >0

Vậy 2x^2-7=11

2x^2=16

x^2=4

Vậy x=2 hoặc -2