A = 2017 2018 + 2018 2019 > 2017 2019 + 2018 2019 = 2017 + 2018 2019 > 2017 + 2018 2018 + 2019 = B

A = 2017 2018 + 2018 2019 > 2017 2019 + 2018 2019 = 2017 + 2018 2019 > 2017 + 2018 2018 + 2019 = B

Ta có

A = 2017 2018 + 2018 2019 > 2017 2019 + 2018 2019 = 2018 + 2018 2019

Mà  2017 + 2018 2019 > 2017 + 2018 2018 + 2019 = B

Nên A > B

a: <

b: <

c: =

\(a,17< 23\Rightarrow333^{17}< 333^{23}\\ b,2007< 2008\Rightarrow2007^{10}< 2008^{10}\\ c,\left(2008-2007\right)^{2009}=1^{2009}=1^{1999}=\left(1998-1997\right)^{1999}\)

A=B (do 2 phân số giống nhau)

Ta có: \(A=\dfrac{2000}{2001}+\dfrac{2001}{2002}\)và\(B=\dfrac{2000}{2001}+\dfrac{2001}{2002}\)

Mà\(\dfrac{2000}{2001}+\dfrac{2001}{2002}=\dfrac{2000}{2001}+\dfrac{2001}{2002}\)

Vậy A=B

Đáp án cần chọn là: A

Dễ thấy A < 1 nên:

A = 2018 2018 + 1 2018 2019 + 1 < 2018 2018 + 1 + 2017 2018 2019 + 1 + 2017 = 2018 2018 + 2018 2018 2019 + 2018 = 2018. 2018 2017 + 1 2018. 2018 2018 + 1 = 2018 2017 + 1 2018 2018 + 1 = B

Vậy A < B

A = 2018 2019 + 2019 2020 > 2018 2020 + 2019 2020 = 2018 + 2019 2020 > 2018 + 2019 2019 + 2020 = B

Vậy A > B

Ta có:

\(\frac{2018+2019}{2019+2020}=\frac{2018}{2019+2020}+\frac{2019}{2019+2020}\)

\(\frac{2018}{2019}>\frac{2018}{2019+2020}\)

\(\frac{2019}{2020}>\frac{2019}{2019+2020}\)

Vậy: A>B

a=b  vì a tách ra thành tích có thừa số là 100010001

 b tách ra thành tích có thừa số là 100010001

A > B

xét 1222 của A lớn hơn 133 của B là 1089

1000 của A bé hơn 1111 của B là 111

xuy ra A > B

\(A=1222\times1000=1222000\)

\(B=133\times11=14763\)

Mà : \(1222000>14763\)

\(\Rightarrow A< B\)

a: \(A=1999\cdot2001\)

\(=\left(2000-1\right)\left(2000+1\right)\)

\(=2000^2-1=B-1\)

=>A<B

b: \(B=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\)

\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\)

\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\)

\(=\left(2^8-1\right)\left(2^8+1\right)=2^{16}-1\)

=A-1

=>B<A

c: \(A=2011\cdot2013\)

\(=\left(2012-1\right)\left(2012+1\right)=2012^2-1\)

=B-1

=>A<B

d: \(A=4\left(3^2+1\right)\left(3^4+1\right)\cdot\ldots\cdot\left(3^{64}+1\right)\)

\(=\frac12\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\cdot\ldots\cdot\left(3^{64}+1\right)\)

\(=\frac12\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\cdot\ldots\cdot\left(3^{64}+1\right)\)

\(=\frac12\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)\cdot\left(3^{32}+1\right)\cdot\left(3^{64}+1\right)\)

\(=\frac12\left(3^{16}-1\right)\left(3^{16}+1\right)\cdot\left(3^{32}+1\right)\cdot\left(3^{64}+1\right)\)

\(=\frac12\left(3^{32}-1\right)\cdot\left(3^{32}+1\right)\cdot\left(3^{64}+1\right)\)

\(=\frac12\left(3^{64}-1\right)\cdot\left(3^{64}+1\right)=\frac12\left(3^{128}-1\right)\)

=1/2B

=>A<B