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a)
\(2^x\left(1+2+2^2+2^3\right)=480\)
\(2^x.15=480\Rightarrow2^x=\frac{480}{15}=32=2^5\Rightarrow x=5\)
a.N=1-5-9+13+17-21+...+2001-2005-2009+2013+2017
N = ( 1 - 5 - 9 + 13 ) + ( 17 - 21 - 25 + 29 ) + .... + ( 2001 - 2005 - 2009 + 2013 ) + 2017
N = 0 + 0 + ... + 0 + 2017
N = 2017
\(\left(\frac{x+2015}{2014}-1\right)+\left(\frac{x+2015}{2013}-1\right)+\left(\frac{x+2015}{2012}-1\right)=3\left(\frac{x+2015}{2011}-1\right)\)
\(\frac{x+2015}{2014}+\frac{x+2015}{2013}+\frac{x+2015}{2012}=\frac{3\left(x+2015\right)}{2011}\)
\(\frac{x+2015}{2014}+\frac{x+2015}{2013}+\frac{x+2015}{2012}-\frac{x+2015}{2011}+\frac{x+2015}{2011}+\frac{x+2015}{2011}=0\)
\(\left(x+2015\right)\left(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2011}+\frac{1}{2011}+\frac{1}{2011}\right)=0\)
\(x+2015=0\text{ Vì }\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2011}+\frac{1}{2011}+\frac{1}{2011}\ne0\)
\(x=-2015\)
TA CÓ: \(\frac{x}{2013}+\frac{x-1}{2012}=\frac{x-2}{2011}+\frac{x-3}{2010}\)
\(\Rightarrow\frac{x}{2013}+\frac{x-1}{2012}-\frac{x-2}{2011}-\frac{x-3}{2010}=0\)
\(\frac{x}{2013}-1+\frac{x-1}{2012}-1-\frac{x-2}{2011}+1-\frac{x-3}{2010}+1=0\)
\(\left(\frac{x}{2013}-1\right)+\left(\frac{x-1}{2012}-1\right)-\left(\frac{x-2}{2011}-1\right)-\left(\frac{x-3}{2010}-1\right)=0\)
\(\frac{x-2013}{2013}+\frac{x-2013}{2012}-\frac{x-2013}{2011}-\frac{x-2013}{2010}=0\)
\(\left(x-2013\right).\left(\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2011}-\frac{1}{2010}\right)=0\)
MÀ \(\frac{1}{2013}< \frac{1}{2011};\frac{1}{2012}< \frac{1}{2010}\)
\(\Rightarrow\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2011}-\frac{1}{2010}\ne0\)
\(\Rightarrow x-2013=0\)
\(x=2013\)
VẬY X= 2013
CHÚC BN NĂM MỚI VUI VẺ NHA!!!!!!!