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26 tháng 5 2017
Tính nhanh :
A = \(2016.20152015-2015.20162016\)
= \(2016.2015.10001-2015.2016.1001\)
=0
26 tháng 5 2017
\(A=2016.20152015-2015.20162016\)
\(=2016.2015.10001-2015.2016.10001\)
\(=0\)
25 tháng 5 2017
A= \(\dfrac{1993\left(1994+1\right)}{1995\left(1992+1\right)}\)=1
25 tháng 5 2017
B=\(\dfrac{399\left(45+55\right)}{1995\left(1996-1991\right)}\)=\(\dfrac{399.5.100}{399.5.5}\)=100
14 tháng 7 2017
\(\dfrac{x+24}{1996}+\dfrac{x+25}{1995}+\dfrac{x+26}{1994}+\dfrac{x+27}{1993}+\dfrac{x+2036}{4}=0\)
\(\Rightarrow\left(\dfrac{x+24}{1996}+1\right)+\left(\dfrac{x+25}{1995}+1\right)+\left(\dfrac{x+26}{1994}+1\right)+\left(\dfrac{x+27}{1993}+1\right)+\left(\dfrac{x+2036}{4}-4\right)=0\)\(\Rightarrow\dfrac{x+2020}{1996}+\dfrac{x+2020}{1995}+\dfrac{x+2020}{1994}+\dfrac{x+2020}{1993}+\dfrac{x+2020}{4}=0\)\(\Rightarrow\left(x+2020\right)\left(\dfrac{1}{9996}+\dfrac{1}{1995}+\dfrac{1}{1994}+\dfrac{1}{1993}+\dfrac{1}{4}\right)=0\)
\(\Rightarrow x+2020=0\Rightarrow x=-2020\)
PM
1
HT
24 tháng 10 2016
a) 2^1993 = (22)996 x2 = 4996 x2 4 mũ chẵn có tận cùng là 6 nên 4996 x2=..4 x2=..8
b) 3^1995 = (32)997 x3 = 9997 x3 9 mũ lẻ có tận cùng là 9 nên 9997 x3=...9 x3 =...7
c) 7^1993 = (72)996 x7 = 49996 x7 9 mũ chẵn có tận cùng là 1 nên 49996 x7=..1 x7 =..7
d) Vì 6 mũ bnhiu cũng có tận cùng là 6 nhá :D
NP
0
4 tháng 7 2017
\(A=\dfrac{1995.1994-1}{1993.1995+1994}=\dfrac{1995\left(1993+1\right)-1}{1993.1995+1994}=\dfrac{1995.1993+1995-1}{1993.1995+1994}=\dfrac{1995.1993+1994}{1995.1993-1994}=1\)\(B=\dfrac{2004.2004+3006}{2005.2005-1003}=\dfrac{2004.2004+2004.1+1002}{2005.2005-1003}=\dfrac{2004.2005+1002}{2005.2005-1003}=\dfrac{2004.2005+1002}{2004.2005+2005-1003}=\dfrac{2004.2005+1002}{2004.2005+1002}=1\)\(C=\dfrac{2010.2011-1}{2009.2011+2010}=\dfrac{2009.2011+2011-1}{2009.2011+2010}=\dfrac{2019.2011+2010}{2009.20011+2010}=1\)\(D=\dfrac{2014.2015-1}{2013.2015+2013}=\dfrac{2013.2015+2014-1}{2013.2015+2013}=\dfrac{2013.2015+2013}{2013.2015+2013}=1\)
LG
4 tháng 7 2017
Câu 1 nhầm đề nha bạn mình sửa:
\(\dfrac{1995.1994-1}{1993.1995+1994}\)
\(=\dfrac{1995.\left(1993+1\right)-1}{1993.1995+1994}\)
\(=\dfrac{1995.1993+1995-1}{1993.1995+1994}\)
\(=\dfrac{1993.1995+1994}{1993.1995+1994}\)
\(=1\)
Câu 2: \(\dfrac{2004.2004+3006}{2005.2005-1003}\)
\(=\dfrac{2004.2004+2004+1002}{\left(2004+1\right).\left(2004+1\right)-1003}\)
\(=\dfrac{2004.2004+2004+1002}{2004.2004+2004+1-1003}\)
\(=\dfrac{2004.2004+2004+1002}{2004.2004+2004+1002}\)
\(=1\)
Câu 3:\(\dfrac{2010.2011-1}{2009.2011+2010}\)
\(=\dfrac{\left(2009+1\right).2011-1}{2009.2011+2010}\)
\(=\dfrac{2009.2011+2011-1}{2009.2011+2010}\)
\(=\dfrac{2009.2011+2010}{2009.2011+2010}\)
= 1
Câu 4:Nhầm để, sửa:
\(\dfrac{2014.2015-1}{2013.2015+2014}\)
\(=\dfrac{\left(2013+1\right).2015-1}{2013.2015+2014}\)
\(=\dfrac{2013.2015+2015-1}{2013.2015+2014}\)
\(=\dfrac{2013.2015+2014}{2013.2015+2014}\)
\(=1\)
NT
3
22 tháng 7 2015
Số các số hạng là:
(1995-1):2+1=998 (số)
Tổng của dãy số trên là:
(1995+1)x998:2=996004
Đáp số: 996004.
12 tháng 4 2016
<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993
<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993
<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993
<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993
<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993
<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993
<=>2.(1/2-1/x+1)=1991/1993
<=>1/2-1/x+1=1991/1993:2=1991/3986
<=> 1/x+1=1/2-1991/3986=2/3986=1/1993
=>x=1993-1=1992
<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993
<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993
<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993
<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993
<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993
<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993
<=>2.(1/2-1/x+1)=1991/1993
<=>1/2-1/x+1=1991/1993:2=1991/3986
<=> 1/x+1=1/2-1991/3986=2/3986=1/1993
=>x=1993-1=1992
<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993
<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993
<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993
<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993
<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993
<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993
<=>2.(1/2-1/x+1)=1991/1993
<=>1/2-1/x+1=1991/1993:2=1991/3986
<=> 1/x+1=1/2-1991/3986=2/3986=1/1993
=>x=1993-1=1992
<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993
<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993
<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993
<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993
<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993
<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993
<=>2.(1/2-1/x+1)=1991/1993
<=>1/2-1/x+1=1991/1993:2=1991/3986
<=> 1/x+1=1/2-1991/3986=2/3986=1/1993
=>x=1993-1=1992
<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993
<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993
<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993
<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993
<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993
<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993
<=>2.(1/2-1/x+1)=1991/1993
<=>1/2-1/x+1=1991/1993:2=1991/3986
<=> 1/x+1=1/2-1991/3986=2/3986=1/1993
=>x=1993-1=1992
<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993
<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993
<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993
<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993
<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993
<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993
<=>2.(1/2-1/x+1)=1991/1993
<=>1/2-1/x+1=1991/1993:2=1991/3986
<=> 1/x+1=1/2-1991/3986=2/3986=1/1993
=>x=1993-1=1992
<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993
<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993
<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993
<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993
<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993
<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993
<=>2.(1/2-1/x+1)=1991/1993
<=>1/2-1/x+1=1991/1993:2=1991/3986
<=> 1/x+1=1/2-1991/3986=2/3986=1/1993
=>x=1993-1=1992
<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993
<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993
<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993
<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993
<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993
<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993
<=>2.(1/2-1/x+1)=1991/1993
<=>1/2-1/x+1=1991/1993:2=1991/3986
<=> 1/x+1=1/2-1991/3986=2/3986=1/1993
=>x=1993-1=1992
<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993
<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993
<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993
<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993
<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993
<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993
<=>2.(1/2-1/x+1)=1991/1993
<=>1/2-1/x+1=1991/1993:2=1991/3986
<=> 1/x+1=1/2-1991/3986=2/3986=1/1993
=>x=1993-1=1992
<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993
<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993
<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993
<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993
<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993
<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993
<=>2.(1/2-1/x+1)=1991/1993
<=>1/2-1/x+1=1991/1993:2=1991/3986
<=> 1/x+1=1/2-1991/3986=2/3986=1/1993
=>x=1993-1=1992
<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993
<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993
<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993
<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993
<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993
<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993
<=>2.(1/2-1/x+1)=1991/1993
<=>1/2-1/x+1=1991/1993:2=1991/3986
<=> 1/x+1=1/2-1991/3986=2/3986=1/1993
=>x=1993-1=1992
<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993
<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993
<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993
<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993
<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993
<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993
<=>2.(1/2-1/x+1)=1991/1993
<=>1/2-1/x+1=1991/1993:2=1991/3986
<=> 1/x+1=1/2-1991/3986=2/3986=1/1993
=>x=1993-1=1992
<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993
<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993
<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993
<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993
<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993
<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993
<=>2.(1/2-1/x+1)=1991/1993
<=>1/2-1/x+1=1991/1993:2=1991/3986
<=> 1/x+1=1/2-1991/3986=2/3986=1/1993
=>x=1993-1=1992
<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993
<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993
<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993
<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993
<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993
<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993
<=>2.(1/2-1/x+1)=1991/1993
<=>1/2-1/x+1=1991/1993:2=1991/3986
<=> 1/x+1=1/2-1991/3986=2/3986=1/1993
=>x=1993-1=1992
<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993
<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993
<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993
<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993
<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993
<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993
<=>2.(1/2-1/x+1)=1991/1993
<=>1/2-1/x+1=1991/1993:2=1991/3986
<=> 1/x+1=1/2-1991/3986=2/3986=1/1993
=>x=1993-1=1992
<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993
<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993
<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993
<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993
<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993
<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993
<=>2.(1/2-1/x+1)=1991/1993
<=>1/2-1/x+1=1991/1993:2=1991/3986
<=> 1/x+1=1/2-1991/3986=2/3986=1/1993
=>x=1993-1=1992
<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993
<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993
<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993
<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993
<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993
<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993
<=>2.(1/2-1/x+1)=1991/1993
<=>1/2-1/x+1=1991/1993:2=1991/3986
<=> 1/x+1=1/2-1991/3986=2/3986=1/1993
=>x=1993-1=1992
<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993
<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993
<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993
<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993
<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993
<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993
<=>2.(1/2-1/x+1)=1991/1993
<=>1/2-1/x+1=1991/1993:2=1991/3986
<=> 1/x+1=1/2-1991/3986=2/3986=1/1993
=>x=1993-1=1992
NC
2
MH
16 tháng 7 2015
(1+3+5+7+...+1995)+2x=996006
[(1995+1).998 : 2] + 2x = 996006
996004+2x=996006
=> 2x = 2
=> x=1
16 tháng 7 2015
(1+3+5+7+...+1995)+2x=996006
[(1995+1).998 : 2] + 2x = 996006
996004+2x=996006
=> 2x = 2
=> x=1
NT
0
\(\dfrac{1993+1993.1994}{1992.1995+1995}\)
=\(\dfrac{1993.1+1993.1994}{1992.1995+1995.1}\)
=\(\dfrac{1993\left(1+1994\right)}{1995\left(1992+1\right)}\)
=\(\dfrac{1993.1995}{1995.1993}\)
=1
\(=\dfrac{1993.1+1993.1994}{1992.1995+1995.1}\)
\(=\dfrac{1993\left(1+1994\right)}{1995\left(1992+1\right)}\)
\(=\dfrac{1993.1995}{1995.1993}\)
=1