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\(A=1-5-9+13+17-21-25+29+.......+2001-2005-2009+2013+2017\)\(A=\left(1-5-9+13\right)+.........+\left(2001-2005-2009+2013\right)+2017\)
\(A=0+0+...............+2017\)
\(A=2017\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Số hạng tử là:
( 2013 - 1 ) : 4 + 1 = 504 ( hạng tử )
N = ( 1 - 5 - 9 + 13 ) + ( 17 - 21 - 25 + 29 ) + ... + ( 2001 - 2005 - 2009 +2013 )
N = 0
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Gọi A=1-5-9+13+17-21-25+........+2001-2005-2009+2013
A có số số hạng là: (2013 -1):4+1= 504 (số hạng)
Ta có: A= 1-5-9+13+17-21-25+..........+2001 - 2005 - 2009+2013
A= (1-5)+(-9+13)+(17-21)+(-25+29)+............+(2001-2005) + (-2009+2013)
A= (-4)+4+(-4)+4+..........+(-4)+4 (504 số hạng)
A= [(-4)+4]+[(-4)+4]+..........+[(-4)+4] (252 nhóm)
A= 0.252
A= 0
Vậy 1-5-9+13+17-21-25+..........+2001-2005-2009+2013 = 0
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
N=1-5-9+13+17-21-25+...+2001-2005-2009+2013
N=(1-5-9+13)+(17-21-25+29)+,,,,,+(2001-2005-2009+2013)
N=0+0+.....+0
N=0
Vay N=0
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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
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a) -1 - 2 - 3 - 4 - 5 -.............- 2009 - 2010
SCSH: ( 2010 - 1 ) : 1 + 1 = 2010
tỔNG: ( 2010 + 1 ) . 2010 : 2 = 2021055
b) 1 - 3 + 5 - 7 +...............+ 2005 - 2007 + 2009 - 2011
SCSH: ( 2011 - 1 ) : 2 + 1 = 1006
tỔNG: ( 2011 + 1 ) . 1006 : 2 = 1012036
c) 1 - 2 - 3 + 4 + 5 - 6 - 7 +..........................+ 1997 - 1998 - 1999 + 2000 + 2001
SCSH: ( 2001 - 1 ) : 1 + 1 = 2001
tỔNG: ( 2001 + 1 ) . 2001 : 2 = 2003001
Hk tốt,
k nhé
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 2 :
Ta có :
\(A=1+3+3^2+...+3^{2012}\)
\(3A=3+3^2+3^3+...+3^{2013}\)
\(3A-A=\left(3+3^2+3^3+...+3^{2013}\right)-\left(1+3+3^2+...+3^{2012}\right)\)
\(2A=3^{2013}-1\)
\(A=\frac{3^{2013}-1}{2}\)
\(\Rightarrow\)\(A-B=\frac{3^{2013}-1}{2}-\frac{3^{2013}}{2}=\frac{3^{2013}-1-3^{2013}}{2}=\frac{-1}{2}\)
Vậy \(A-B=\frac{-1}{2}\)
Chúc bạn học tốt ~
= ( 2013 - 2009 ) + ( 2005 - 2001 ) + ( 1997 - 1993 ) + ...+ ( 29 - 25 )
= 4 + 4 + 4 + ...+ 4
= 4 * 249
= 996