1-2-3+4+5-6-7+8+...+1993-1994
1-2-3+4+5-6-7+8+...+1993-1994
\(\left(1-2-3+4\right)+\left(5-6-7+8\right)+...+\left(1993-1994\right)\)
\(=0+0+....+\left(-1\right)\)
\(=\left(-1\right)\)
Ta có 1-2-3+4+5-6-7+8+...+1993-1994
=(1-2-3+4)+(5-6-7+8)+...+(1889-1990-1991+1992)+1993-1994
= 0 + +0 +.....+ 0 + 1993-1994
= -1
M= 1-2-3+4+5-6-7+8+...........+1993-1994-1995+1996+1997.
A=1-3+5-7+...+2019-2021+2023
B=1-2-3+4+5-6-7+8+...+1993-1994
A=1-3+5-7+...+2019-2021+2023
A = 1 + 5 + .. .+ 2019 + 2023 - 3 - 7 - ... - 2017 - 2021
A = ( 1 + 5 + ... + 2023 ) - ( 3 + 7 + ... + 2021 )
A = 512578
Tính các tổng sau
a) A = 1 – 3 + 5 – 7 + … + 2001 – 2003 + 2005. b) B = 1 – 2 – 3 + 4 + 5 – 6 - 7 + 8 + …+ 1993 – 1994.
Lời giải:
a.
$A=(1-3)+(5-7)+(9-11)+...+(2001-2003)+2005$
$=(-2)+(-2)+(-2)+...+(-2)+2005$
$=(-2).501+2005=-1002+2005=1003$
b.
$B=(1-2-3+4)+(5-6-7+8)+...+(1989-1990-1991+1992)+(1993-1994)$
$=0+0+....+0+(1993-1994)=0+(-1)=-1$
Tính:
a) 1-3+5-7+...+2001-2003+2005
b) 1-2-3+4+5-6-7+8+...+1993-1994
A=1-3+5-7+...+2001-2003+2005
B=1-2-3+4+5-6-7+8+...+1993-1994
C=1+2-3-4+5+6-7-8+9+...+2002-2003-2004+2005+2006
A=1-3+5-7+....+2001-2003+2005
A=[(1-3)+(5-7)+.....+(2001-2003)]+2005
A=[(-2)+(-2)+....+(-2)]+2005
Vì từ 1 đến 2003 có: 1002 số hạng => có 501 cặp => có 501 số -2
A=(-2) x 501 +2005
A=-1002+2005
A=1003
A=1-3+5-7+...+2001-2003+2005
A=(1-3)+(5-7)+....+(2001-2003)+2005
A=(-2)+(-2)+...+(-2)+2005
A=(-2).501+2005
A=(-1002)+2005
A=1003
B=1-2-3+4+5-6-7+8+...+1993-1994
B=(1-2-3+4)+(5-6-7+8)+....+(1989-1990-1991+1992)+(1993-1994)
B=0+0+...+0+(-1)
B=(-1)
C=1+2-3-4+5+6-7-8+9+...+2002-2003-2004+2005+2006
C=(1+2-3-4)+(5+6-7-8)+....+(2001+2002-2003-2004)+(2005+2006)
C=(-4)+(-4)+....+(-4)+4011
C=(-4).501+4011
C=(-2004)+4011
C=2007
A=1-3+5-7+...+2001-2003+2005
A= (-2) + (-2) +....+(-2) +2005
A= -2. 501 +2005
A= -1002 +2005
A= 1003
B=1-2-3+4+5-6-7+8+...+1993-1994
B= (1-2-3+4) + (5-6-7 +8) +.......+ (1989 - 1990 -1991 +1992)+1993-1994
B= 0 + 0+....+0+ 1993-1994
B= -1
C=1+2-3-4+5+6-7-8+9+...+2002-2003-2004+2005+2006
C= (1+2-3-4) + (5+6-7-8) +.....+(2001+2002 -2003 -2004) +2005+2006
C= -4. 501 + 2005 +2006
C= -2004+2005+2006
C= 2007
Tinh nhanh: M=1-2-3+4+5-6-7+8+...+1993-1994-1995+1996+1997
Tính nhanh: M=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
=0+0+....+0+1997
=1997
Tính nhanh:
M=1-2-3+4+5-6-7+8+...+1993-1994-1995+1996+1997