=1+(2-3-4+5)+3-4-5+6)+...+(200-201-202+203)+204

=1+0+0+...+0+204

=1+204

=205

tinh 

1+2 -3 -4 +5+3-4-5+6 +4-5-6 +7 + ....+200-201 -202 + 203 + 204 =1+0+...+0+204=1+204=205.

bn k cho mik nha. ^-^ thanks bn trc.

ban oi minh chua hoc so am 

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

Sửa đề     \(1-2+3-4+5-6+7-8+...+201-202+203\)

Đặt \(A=1-2+3-4+5-6+7-8+...+201-202+203\)

ta có từ 1 đến 202 có 202 số hạng. nhóm 2 số thành một nhóm ta có  \(202\div2=101(\)nhóm\()\)

\(\Rightarrow\)\(A=(1-2)+(3-4)+(5-6)+(7-8)+...+(201-202)+203\)

\(A=(-1-1-1-1-...-1)+203\) 

\(A=-101+203\)

\(A=102\)

Vậy A =102

chúc bạn học tốt

cách tốt nhất để tính đó chính là ..................................................................................................................................................................................................................................................................................................................sử dụng máy tính cầm tay

1-2+3-4+5-6+7-8+...+201-202+203

= ( -1 )+ ( -1 ) +(-1 ) + (-1 ) +... + (-1 ) + 203

= (-1 ). \([\) ( 202 - 1 ) : 1 + 1 \(]\):2  + 203

= (-1 ) . 101 + 203

= -202 + 203

= 1

199 - 200 + 201 - 202 + 203 - 204 + 205 - 206 + 207

= ( 199 - 200 ) + ( 201 - 202 ) + ( 203 - 204 ) + ( 205 - 206 ) + 207

= ( -1 ) + ( -1 ) + ( -1 ) + ( -1 ) + 207

= -4 + 207

= 203

199 - 200 + 201 - 202 + 203 - 204 + 205 - 206 + 207 = 203 

199-200+201-202+203-204+205-206+207

=203

Tính nhanh:

a) 1-2-3+4+5-6-7+8+9-10-.......+200+201-202-203

Đặt \(A=\text{1-2-3+4+5-6-7+8+9-10-.......+200+201-202-203}\)

\(A=1+\left(2-3-4+5\right)+\left(6-7-8=9\right)+\left(10-11-12+13\right)+... \)\(+\left(298-299-300+301\right)+302\)

\(A=1+0+0+0+...+0+302\)

\(A=1+302\)

\(A=303\)

Phần B làm sau nha!

em nên gõ công thức trực quan để được hỗ trợ tốt nhất nhé

       D =           \(\dfrac{1}{7^2}\) - \(\dfrac{2}{7^3}\) + \(\dfrac{3}{7^4}\) - \(\dfrac{4}{7^5}\) +........+ \(\dfrac{201}{7^{202}}\) -  \(\dfrac{202}{7^{203}}\)

7 \(\times\) D  =  \(\dfrac{1}{7}\) -  \(\dfrac{2}{7^2}\) +  \(\dfrac{3}{7^3}\) - \(\dfrac{4}{7^4}\)  + \(\dfrac{5}{7^5}\) -.......- \(\dfrac{202}{7^{202}}\)

7D +D  =   \(\dfrac{1}{7}\) - \(\dfrac{1}{7^2}\) + \(\dfrac{1}{7^3}\) - \(\dfrac{1}{7^4}\) + \(\dfrac{1}{7^5}\) -.........-\(\dfrac{1}{7^{202}}\) - \(\dfrac{202}{7^{203}}\)

         D = (  \(\dfrac{1}{7}\) - \(\dfrac{1}{7^2}\) + \(\dfrac{1}{7^3}\) - \(\dfrac{1}{7^4}\) + \(\dfrac{1}{7^5}\) -.........-\(\dfrac{1}{7^{202}}\) - \(\dfrac{202}{7^{203}}\)) : 8

Đặt    B =      \(\dfrac{1}{7}\) - \(\dfrac{1}{7^2}\) + \(\dfrac{1}{7^3}\) - \(\dfrac{1}{7^4}\) + \(\dfrac{1}{7^5}\) -........+\(\dfrac{1}{7^{201}}\).-\(\dfrac{1}{7^{202}}\) 

  7   \(\times\) B = 1 - \(\dfrac{1}{7}\)+\(\dfrac{1}{7^2}\) - \(\dfrac{1}{7^3}\) + \(\dfrac{1}{7^4}\) - \(\dfrac{1}{7^5}\) +.........- \(\dfrac{1}{7^{201}}\)

7B + B   =  1 - \(\dfrac{1}{7^{202}}\)

          B   =  ( 1 - \(\dfrac{1}{7^{202}}\)) : 8

         D  =  [ ( 1 - \(\dfrac{1}{7^{202}}\)): 8  - \(\dfrac{202}{7^{203}}\)] : 8 

          D = \(\dfrac{1}{64}\) - \(\dfrac{1}{64.7^{202}}\) - \(\dfrac{202}{7^{203}.8}\) < \(\dfrac{1}{64}\)

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