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18 tháng 12 2019

2019.5+2019:0,1+2019+2019:0,25

= 10095 + 20190 + 2019 + 8076

= 30285+2019+8076

= 32304+8076

= 40380

18 tháng 12 2019

Tính nhanh hay thực hiện phép tính bạn

AH
Akai Haruma
Giáo viên
14 tháng 5 2021

Lời giải:

Ta có: 

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

\(B+1=\frac{2019^{2019}+2019^{2018}}{2019^{2018}-1}=\frac{2019^{2018}.2020}{2019^{2018}-1}\) \(=\frac{2019^{2019}.2020}{2019^{2019}-2019}>\frac{2019^{2019}.2020}{2019^{2019}-1}\)

$\Rightarrow B+1>A+1$

$\Rightarrow B>A$

+)Ta có:\(A=2019+2019^2+2019^3+2019^4+2019^5+2019^6\)

\(\Rightarrow A=\left(2019+2019^2\right)+\left(2019^3+2019^4\right)+\left(2019^5+2019^6\right)\)

\(\Rightarrow A=\left(2019+2019^2\right)+2019^2.\left(2019+2019^2\right)+2019^4.\left(2019+2019^2\right)\)

+)Ta lại có:20192 tận cùng là 1

=>2019+20192 tân cùng là 9+1=10

=>2019+20192\(⋮2\)

\(\Rightarrow\left(2019+2019^2\right)⋮2;2019^2.\left(2019+2019^2\right)⋮2;2019^4.\left(2019+2019^2\right)⋮2\)

\(\Rightarrow A⋮2\)

Vậy \(A⋮2\left(ĐPCM\right)\)

Chúc bn học tốt

10 tháng 3 2020

A = 2019 + 20192 + 20193 + 20194 + 20195 + 20196

A = ( 2019 + 20192 ) + ( 20193 + 20194) + ( 20195 + 20196)

A = 1 . ( 2019 + 20192 ) + 20193 . (2019 + 20192 ) + 20195 . ( 2019 + 20192 )

A = 1 . 4 078 380   + 20193 . 4 078 380 + 20195 . 4 078 380

A = 4 078 380 . ( 1 + 20193 + 20195\(⋮2\rightarrowĐPCM\)

# HOK TỐT #

28 tháng 12 2020

Vì 2019 + 2020 < 2019 + 2021 nên A < B

Ta có: \(A=\left(2020^{2019}+2019^{2019}\right)^{2020}\)

\(=\left(2019^{2019}+2020^{2019}\right)^{2019}\cdot\left(2019^{2019}+2020^{2019}\right)\)

\(\Leftrightarrow\dfrac{A}{B}=\dfrac{\left(2019^{2019}+2020^{2019}\right)^{2019}\cdot\left(2019^{2019}+2020^{2019}\right)}{\left(2020^{2020}+2019^{2020}\right)^{2019}}\)

\(\Leftrightarrow\dfrac{A}{B}=\dfrac{2019^{2019}+2020^{2019}}{2019+2020}>1\)

\(\Leftrightarrow A>B\)

15 tháng 5 2019

\(\frac{2019}{210}+\frac{2019}{280}+\frac{2019}{360}+\frac{2019}{450}+\frac{2019}{550}\)

\(=\frac{673}{70}+\frac{2019}{280}+\frac{673}{120}+\frac{673}{150}+\frac{2019}{550}\)

\(=\left[\frac{673}{70}+\frac{2019}{280}\right]+\frac{673}{120}+\frac{673}{150}+\frac{2019}{550}\)

\(=\left[\frac{2692}{280}+\frac{2019}{280}\right]+\frac{673}{120}+\frac{673}{150}+\frac{2019}{550}\)

\(=\frac{673}{40}+\frac{673}{120}+\frac{673}{150}+\frac{2019}{550}\)

\(=\left[\frac{673}{40}+\frac{673}{120}\right]+\frac{673}{150}+\frac{2019}{550}\)

\(=\left[\frac{2019}{120}+\frac{673}{120}\right]+\frac{673}{150}+\frac{2019}{550}\)

\(=\frac{673}{30}+\frac{673}{150}+\frac{2019}{550}\)

\(=\left[\frac{673}{30}+\frac{673}{150}\right]+\frac{2019}{550}\)

\(=\frac{673}{25}+\frac{2019}{550}=\frac{14806}{550}+\frac{2019}{550}=\frac{16825}{550}=\frac{673}{22}\)

P/S : Các a chị check dùm em ạ

( - 2019 - 2019 - 2019 - 2019 ) x ( -25 ) 

= (-4 ) x 2019 x ( - 25 ) 

= ( -4 ) x ( -25 ) 2019 

= 100 x 2019 

= 201900 

học tốt 

17 tháng 4 2021

Ta có: B = (2018 + 2019)/(2019 + 2020) = (2018 + 2019)/4039 = 2018/4039 + 2019/4039
Ta thấy : 2018/2019 > 2018/4039
            2019/2020 > 2019/4039
=> 2018/2019 + 2019/2020 > 2018/4039 > 2019/4039
=> 2018/2019 + 2019/2020 > (2018 + 2019)/(2019 + 2020)
=> A  > B

11 tháng 5 2019

\(A=\frac{2018^{2019}-1}{2018^{2019}+1}=\frac{2018^{2019}+1-2}{2018^{2019}+1}=\frac{2018^{2019}+1}{2018^{2019}+1}-\frac{2}{2018^{2019}+1}=1-\frac{2}{2018^{2019}+1}\)

\(B=\frac{2018^{2019}}{2018^{2019}+2}=\frac{2018^{2019}+2-2}{2018^{2019}+2}=\frac{2018^{2019}+2}{2018^{2019}+2}-\frac{2}{2018^{2019}+2}=1-\frac{2}{2018^{2019}+2}\)

Ta có: \(\frac{2}{2018^{2019}+1}>\frac{2}{2018^{2019}+2}\)

\(\Rightarrow1-\frac{2}{2018^{2019}+1}< 1-\frac{2}{2018^{2019}+2}\)

\(\Rightarrow A< B\)

Vậy .....