Tính tổng:
M = 1+(-2)+3+(-4)+...+2001+(-2002)
M = 1+2+(-3)+4-....-1999+2000
Tính tổng:
M=1+(-2)+3+(-4)+...+2001+(-2002)
M=-1+2+(-3)+4-...-1999+2000
Tính tổng:
h) – 1- 2 – 3 – 4 – 5 - … - 1999 – 2000 – 2001 – 2002
h) -1 - 2 - 3 - 4 - 5 - ..... - 1999 - 2000 - 2001 - 2002
A= -(1 + 2 + 3+...+ 2002) có 2002 số hạng
A= -(2002+2001+2000+...+2+1)
2A=-(1+2002) .2002
A=-2003.1001 =-2005003
tính : A=1+2-3-4+5+6-7-8+...-1999-2000+2001+2002-2003
A=(1+2-3)+(-4+5+6-7)+(-8+9+10-11)+......(-2000+2001+2002-2003)
A=0+0....+0
A=0
Ta thấy 2-3-4=-5
6-7-8=-9
.............
1998-1999-2000=-2001
=> 1+2-3-4+5+6-7-8+....-1999-2000+2001-2003=1-5+5-9+9-...-2001+2001+2002-2003
=> A= 1+2002-2003=0
Vậy A=0
\(=\left(1+2-3\right)+\left(-4+5+6-7\right)+...+\left(-2000+2001+2002-2003\right)\)
\(=0+0+0+...+0\)
\(=0\)
học tốt
Tính nhanh
S = 1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + 10 - ...... + 1998 - 1999 - 2000 + 2001 + 2002
S = 1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + 10 - ...... + 1998 - 1999 - 2000 + 2001 + 2002
S = 1 + (2 - 3 - 4 + 5 )+ (6 - 7 - 8 + 9) + (10 - ...... + (1998 - 1999 - 2000 + 2001) + 2002
S=1+0+0...+0+2002
S= 1+2002
S=2003
Lời giải:
$S=(1+2-3-4)+(5+6-7-8)+(9+10-11-12)+...+(1997+1998-1999-2000)+2001+2002$
$=\underbrace{(-4)+(-4)+....+(-4)}_{500}+2001+2002$
$=(-4).500+2001+2002=2003$
`S = 1+2-3-5+5+6-7-8+9+10-...+1998-1999-2000+2001+2002`
có :
`(2002 - 1) :1 +1 = 2002` ( số hạng)
`2002 : 4 = 500 (dư 2)`
`=(1+2-3-4)+(5+6-7-8)+(9+10-11-12)+...+(1997+1998-1999-2000)+2001+2002`
`=(-4)+(-4)+...+(-4) +2001 +2002` có `500` só `-4`
`=500 .(-4) + 2001+ 2002`
`= (-2000)+2001+2002`
`=1+2002`
`=2003`
tính tổng
s1 =1+(-2) +3(-4)+......+2001+(-2002)
s2 =1+(-3) +5+(-7) +....+(-1999)+2001
s3 =1+(-2)+(-3)+4+5+(-6)+(-7)+......+1997+(-1998)+(-1999)+2000
-1-2-3-4-5....-1999-2000-2001-2002
-1 - 2 - 3 - 4 - 5 - .... - 1999 - 2000 - 2001 - 2002
Ta có : -1 - 2 - 3 - 4 - 5 - .... - 1999 - 2000 - 2001 - 2002
= - (1 + 2 + 3 + 4 + ... + 2000 + 2001 + 2002) (có 2002 số )
= - [(2002 + 1) . 2002 : 2]
= - 2005003
tính nhanh (2004^2 + 2002^2 + 2000^2 +...+ 4^2 + 2^2) - (2003^2 + 2001^2 + 1999^2 +...+ 5^2 + 3^2 + 1)
=2004^2-2003^2+2002^2-2001^2+....+1
=(2004+2003)(2004-2003)+(2002+2001)(2002-2001)+.....+1
=2004+2003+...+1
=2009010
Tính tổng :
a) S1 = 1 + (-2) + 3 + (-4) + ... + 2001 + (-2002)
b) S2 = 1 + (-3) + 5 = (-7) + ... + (-1999) + 2001
c) S3 = 1 + (-2) + (-3) + 4 + 5 + (-6) + (-7) + 8 + ... + 1997 + (-1008) + (-1999) + 2000
hãy tính tổng S , biết : S = 1+2+ 3+....2000+2001+2002
Tính: \(D=1+2-3-4+5+6-7-8+...-1999-2000+2001+2002-2003\)
D = 1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + ... - 1999 - 2000 + 2001 + 2002 - 2003
D = ( 1 + 2 - 3 - 4 ) + ( 5 + 6 - 7 - 8 ) + ... + ( 1997 + 1998 - 1999 - 2000 ) + 2001 + 2002 - 2003
D = ( -4 ) + ( -4 ) + ... + ( -4 ) + ( 2001 + 2002 - 2003 )
D = ( -4 ) . 500 + 2000
D = -2000 + 2000
D = 0
D = 1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + ............. - 1999 - 2000 + 2001 + 2002 - 2003
D = ( 1 + 2 - 3 - 4 ) + ( 5 + 6 - 7 - 8 ) + ............ + ( 1997 + 1998 - 1999 - 2000 ) + 2001 + 2002 - 2003
D = ( -4 ) + ( -4 ) + .............. + ( -4 ) + ( 2001 + 2002 - 2003 )
D = ( -4 ) . 500 + 2000
D = -2000 + 2000
D = 0