(x+1)+(x+2)+(x+3)+...+(x+2013)=20132014
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Tìm x :
(x+1)+(x+2)+(x+3)+...+(x+2013)=20132014
\((x+1)+(x+2)+(x+3)+...+(x+2013)=20132014\)
\(x+1+x+2+x+3+...+x+2013=20132014\)
\(2013x+(1+2+3+...+2013)=20132014\)
\(2013x+\dfrac{2013\left(2013+1\right)}{2}=20132014\)
\(2013x+2027091=20132014\)
\(2013x=20132014-2027091\)
\(2013x=18104923\)
\(x=18104923:2013\)
\(x=8994\)(kq đã làm tròn)
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Ta có : \(\left(x+1\right)+\left(x+2\right)+...+\left(x+2013\right)=20132014\)
\(\Leftrightarrow\left(x+x+...+x\right)+\left(1+2+...+2013\right)=20132014\)
\(\Leftrightarrow2013x+\dfrac{2013\left(2013+1\right)}{2}=20132014\)
\(\Leftrightarrow2013x+2027091=20132014\)
\(\Leftrightarrow2013x=18104923\)
\(\Leftrightarrow x=\) (chỗ nãy bẫm mãy tính ra số ngộ quá @@ nên ko ghi vào )
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1.Tính:
1000+999-998+997+...+48-47
2.Tìm các chữ số a,b,c sao cho:
2001a+2004b+2007c=20132014
3. Tìm x :
5^x-1 - 5^x=100
Tính S= \(\dfrac{\left(x^2+x-3\right)^{2013}}{\left(x^5+x^4-x^3-2\right)^{2013}}+\left(x^5+x^4-x^3+1\right)^{2013}\)
với x=\(\dfrac{\sqrt{5}-1}{2}\)
Tính:
$\frac{\frac{2013}{2}+\frac{2013}{3}+\frac{2013}{4}+......+\frac{2013}{2014}}{\frac{2013}{1}+\frac{2012}{2}+\frac{2011}{3}+......+\frac{1}{2013}}$20132 +20133 +20134 +......+20132014 20131 +20122 +20113 +......+12013
Hãy chứng minh A = B , biết:
A = 1 + (1+ 2) + (1+ 2+ 3) + ...........+ ( 1+ 2+ 3+ 4+ ...+ 2013)
B = 2013 x 1 + 2012 x 2 + 2011 x 3 + ......+ 2 x 2012 + 1 x 2013
Bài 2: Tìm x, biết:
a)5(x + 3)-2(3 + x) = 0
b)6x(x2 - 2) - (2 - x2) = 0
c)4x(x - 2013) - x + 2013 = 0
d)(x + 1)2 = x + 1
\(a,\Leftrightarrow3\left(x+3\right)=0\Leftrightarrow x=-3\\ b,\Leftrightarrow\left(x^2-2\right)\left(6x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x^2=2\\6x=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{2}\\x=-\sqrt{2}\\x=-\dfrac{1}{6}\end{matrix}\right.\\ c,\Leftrightarrow\left(x-2013\right)\left(4x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=2013\\x=\dfrac{1}{4}\end{matrix}\right.\\ d,\Leftrightarrow\left(x+1\right)^2-\left(x+1\right)=0\\ \Leftrightarrow\left(x+1\right)\left(x+1-1\right)=0\\ \Leftrightarrow x\left(x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)
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1 x 2 x 3 x ................x 2012 x 2013 - 1 x 3 x 5 x..............x 2011 x 2013 .
(Làm chi tiết nha)
Ta có : 1 x 2 x 3 x ..... x 2012 x 2013 - 1 x 3 x 5 x ..... x 2011 x 2013
= (1 x 3 x 5 x ..... x 2013) x (2 x 4 x 6 x ..... x 2012) - 1 x 3 x 5 x ..... x 2011 x 2013
= (1 x 3 x 5 x ..... x 2011 x 2013) x (2 x 4 x 6 x ..... x 2012 - 1)
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Giải pt
\(\sqrt{2x+\frac{2013-1}{\sqrt{2-x^2}}}-\sqrt[3]{2014-\frac{2013-1}{\sqrt{2-x^2}}}=\sqrt{x+2013}-\sqrt[3]{x+1}\)
a, x+1/2013+x+1/2014+x+1/2015=x+1/2016+x+1/2017
b,x-1/2013+x-2/2014+x-3/2015=x-4/2016-2