C = 1 + (-3) + 5 + (-7) +...+ 2001 + (-2003)

C= (1 - 2003) + (2001 - 3) + (5 - 1999) + (1997 - 7) +...+ (1001 - 1003)

C= -2002 + 1998 - 1994 + 1990 +....-2

C= (-4) + (-4) +....+ (-4) - 2 (250 cặp (-4) )

C= 250 x (-4) - 2

C= -1000 - 2 = -1002

D = (-1001) + (-1000) + (-999) +...+ 1001 + 1002

D= (1001 - 1001) + (1000 - 1000) +...+ (1-1) + 0 + 1002

D= 0 + 0 +... + 0 + 0 + 1002

D= 1002

\(a,S_3=-2-2-...-2\)

Tổng có \(\left[\left(2003-1\right):2+1\right]:2=501\left(số.hạng\right)\)

\(\Rightarrow S_3=501\cdot\left(-2\right)=-1002\)

\(b,S_4=\left(-1001+1001\right)+\left(-1000+1000\right)+...+\left(-1+1\right)+1002\\ S_4=1002\)

a: \(S_3=1+\left(-3\right)+5+\left(-7\right)+...+2001+\left(-2003\right)\)

=(-2)+(-2)+...+(-2)

=-2004

\(\frac{2000\cdot2001-1001}{1999\cdot2002-999}=\frac{1999\cdot2001+2001-1001}{1999\cdot2001+1999-999}\)

\(=\frac{1999\cdot2001+1000}{1999\cdot2001+1000}=1\)

a) A=1-2-3+4+5-6-7+.....+1996+1997-1998-1999+2000

=(1-2-3+4)+(5-6-7+8)+...+(1997-1998-1999+2000)

=0

b) B=1-3+5-7+....+2001-2003+2005

=(1-3)+(5-7)+...+(2001-2003)+2005

=-2.501+2005

=-1002+2005

=1003

c) C=1-2-3+4+5-6-7+8+.....+1993-1994-1995+1996+1997

=(1-2-3+4)+(5-6-7+8)+...+(1993-1994-1995+1996)+1997

=1997

d) D=1000+998+996+......+10-999-997-995-...-11

=(1000-999)+(998-997)+(996-995)+....+(12-11)+10

=1.495+10

=595

a/57x23+23x44-23

57x23+23x44-23x1

=23x(57+44-1)

=23x100

=2300

b

a) 57 . 23 + 23 . 44 - 23

= 57 . 23 + 23 . 44 - 23 . 1

= ( 57 + 44 - 1 ) . 23

= 100 . 23

= 2300

b) 1672 - [ 49 + ( 13 - 7 )³ ]

= 1672 - [ 49 + 6³ ]

= 1672 - [ 49 + 216 ]

= 1672 - 265

= 1407

c) 50 : { 2 . [ 52 - ( 3 . 5 - 2² . 3 )³ ] }

= 50 : { 2 . [ 52 - ( 3 . 5 - 4 . 3 )³ ] }

= 50 : { 2 . [ 52 - ( 3 . 1 )³ ] }

= 50 : { 2 . [ 52 - 27 ] }

= 50 : { 2 . 25 }

= 50 : 50

= 1

d) -2014 + (-999) + 14 + (-2001)

= ( -2014 + 14 ) + [ (-999) + (-2001) ]

= (-2000) + (-3000)

= -5000

Học tốt nhé bạn !