Xét B = \(\frac{201+202+203}{202+203+204}\)

         = \(\frac{201}{202+203+204}\)\(+\)\(\frac{202}{202+203+204}\)\(+\)\(\frac{203}{202+203+204}\)

Vì 202 < 202 + 203 + 204

=> \(\frac{201}{202}\)> \(\frac{201}{202+203+204}\)( 1 )

Vì 203 < 202 + 203 + 204

=> \(\frac{202}{203}\)>\(\frac{202}{202+203+204}\)( 2 )

Vì 204 < 202 + 203 + 204

=> \(\frac{203}{204}\)> \(\frac{203}{202+203+204}\)( 3 )
Cộng vế với vế của ( 1 ), ( 2 ) và ( 3 )

=> \(\frac{201}{202}+\frac{202}{203}+\frac{203}{204}\)> \(\frac{201+202+203}{202+203+204}\)

=> A > B

Vậy A > B

mik cần gấp

Xét B =  \(\frac{201+202+203}{202+203+204}\)

          = \(\frac{201}{202+203+204}\)+ \(\frac{202}{202+203+204}\)+ \(\frac{203}{202+203+204}\)

 Vì 202 < 202 + 203 + 204 nên \(\frac{201}{202}\)>\(\frac{201}{202+203+204}\)(1)

Vì 203 < 202 + 203 + 204 nên \(\frac{202}{203}\)> \(\frac{202}{202+203+204}\)(2)

Vì 204 < 202 + 203 + 204 nên \(\frac{202}{203}\)>\(\frac{202}{202+203+204}\)(3)

Cộng vế vơi vế của (1) , (2) và (3)

=>\(\frac{201}{202}+\frac{202}{203}+\frac{203}{204}\)> \(\frac{201+202+203}{202+203+204}\)

=> A > B

Vậy A > B

202^203<203^202

Ta có :

202²⁰³ = 8 242 408¹⁰¹ ( 1 )

203²⁰² = 42 209¹⁰¹       ( 2 )

Từ ( 1 ) và ( 2 ) suy ra 202²⁰³ < 203²⁰²

vì cơ số 202<cơ số 203 nên 202^203<203^202

..................tên em là jullei Trinh...........................

Ta có : \(202^{203}=(2\cdot101)^{3\cdot101}=(1^3\cdot101^3)^{101}=(8\cdot101\cdot10^{12}\cdot101)=(808\cdot1012)^{101}\)

           \(303^{202}=(3\cdot101)^{2\cdot101}=(32\cdot101^2)^{101}=(9\cdot101^2)^{101}\)

\(\Rightarrow(808\cdot101^2)>(9\cdot101^2)\)

Vậy : 

202³⁰³=(2.101)^3.101=(2³.101³)¹⁰¹=(8.101.101²)¹⁰¹=(808.101²)¹⁰¹

303²⁰²=(3.101)^2.101=(3².101²)¹⁰¹=(9.101²)¹⁰¹

Vì (808.101²)¹⁰¹ > (9.101²)¹⁰¹ suy ra 202³⁰³> 303²⁰²

Vậy.......

a, 202²⁰³=(101.2)²⁰³

=101²⁰³.2²⁰³

=101²⁰².2²⁰².202

b, 203²⁰²=(101,5.2)²⁰²

=101,5²⁰².2²⁰²

còn lại dễ

b, 1990¹⁰+1990⁹=1990⁹.1990+1990⁹=1990⁹.(1990+1)=1990⁹.1991

1991²⁰=1991¹⁹.1991

=>1990¹⁰+1990⁹<1991²⁰

c, 11¹⁹⁷⁹<11¹⁹⁸⁰=(11³)⁶⁶⁰=1331⁶⁶⁰

37¹³²⁰=(37²)⁶⁶⁰=1369⁶⁶⁰

=>11¹⁹⁷⁹<37¹³²⁰

\(S=1\cdot2+2\cdot3+3\cdot4+...+39\cdot40\)

\(3S=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+3\cdot4\cdot\left(5-2\right)+...+39\cdot40\cdot\left(41-38\right)\)

\(3S=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+...+39\cdot40\cdot41-38\cdot39\cdot40\)

\(3S=39\cdot40\cdot41\)\(\Rightarrow S=\dfrac{39\cdot40\cdot41}{3}=21320\)

Ta có : \(S=1.2+2.3+3.4+...+38.39+39.40\)

\(3S=1.2.3+2.3.3+3.4.3+...+38.39.3+39.40.3\)

\(3S=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+39.40.\left(41-38\right)\) \(3S=39.40.41\)

\(S=\dfrac{39.40.41}{3}\)\(=21320\)

S = 1 x 2 + 2 x 3 + 3 x 4 + ... + 38 x 39 + 39 x 40

3S = 1 x 2 x 3 + 2 x 3 x 3 + 3 x 4 x 3 + ... + 38 x 39 x 3 + 39 x 40 x 3

3S = 1 x 2 x 3 + 2 x 3 x ( 4 - 1 ) + 3 x 4 x ( 5 - 2 ) + ... + 38 x 39 x ( 40 - 37 ) + 39 x 40 x ( 41 - 38 )

3S = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + 3 x 4 x 5 - 2 x 3 x 4 + ... + 38 x 39 x 40 - 37 x 38 x 39 + 39 x 40 x 41 - 38 x 39 x 40

S = 39 x 40 x 41 : 3

S = 21320

S=1x2+2x3+3x4+...+38x39+39x40

3S=(1x2+2x3+3x4+...+38x39+39x40)x3

3S=1x2x3+2x3x3+3x4x3+....+39x40x3

3S=1x2x3+2x3x(4-1)+3x4x(5-2)+...+39x40x(41-38)

3S=1x2x3+2x3x4-1x2x3+3x4x5-2x3x4+...+39x40x41-38x39x40

3S=39x40x41

3S=63960

S=63960:3

S=21320

\(202^{303}=\left(2.101\right)^{3.101}=\left(2^3.101^3\right)^{101}=\left(8.101^3\right)^{101}\)

\(303^{202}=\left(3.101\right)^{2.101}=\left(3^2.101^2\right)^{101}=\left(9.101^2\right)^{101}\)

Mà \(8.101^3>9.101^2\)

\(\Rightarrow202^{303}>303^{202}\)

Nếu là violympic

thì cần kq thôi hả

S = 21320

S = 1.2 + 2.3 + 3.4 + ... + 38.39 + 39.40

3S = 1.2.(3-0) + 2.3.(4-1) + 3.4.(5-2) + ... + 38.39.(40-37) + 39.40.(41-38)

3S = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 38.39.40 - 37.38.39 + 39.40.41 - 38.39.40

3S = 39.40.41

S = 13.40.41

S = 21320

S = 1x2+2x3+3x4+ ... + 38x39 + 39 x 40

3S = 1x2x3 + 2x3x3 + 3x4x3 + ... + 38x39x3 + 39x40x3

3S = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + ... + 38x39x( 40-37 ) + 39x40x(41-38)

3S = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + ... + 38x39x40 - 37x38x39 + 39x40x41 - 38x39x40

3S = 39x40x41

S = 39x40x41 : 3

S = 21320