2013+2014x2015
2014x2016-1
Những câu hỏi liên quan
so sanh :A=2013^2012+1/2013^2013+1 va 2013^2013+1/2013^2014+1
Đặt B = 2013^2013+1/2013^2014+1
Ta có: \(B=\frac{2013^{2013}+1}{2013^{2014}+1}< \frac{2013^{2013}+1+2012}{2013^{2014}+1+2012}=\frac{2013^{2013}+2013}{2013^{2014}+2013}=\frac{2013\left(2013^{2012}+1\right)}{2013\left(2013^{2013}+1\right)}=\frac{2013^{2012}+1}{2013^{2013}+1}=A\)
Vậy A > B
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Thực hiện so sánh: A = 2013^2012+1/2013^2013+1
với 2013^2013 +1/ 2013^2014 + 1
CMR nếu 1/a +1/b +1/c = 1/(a+b+c) thì 1/a^2013 + 1/b^2013 + 1/c^2013=1/(a^2013+b^2013+c^2013)
2013+(2013/1+2)+(2013/1+2+3)+(2013/1+2+3+4)+...+(2013/1+2+3+...+2012)
so sanh a va b : a= 2013^2012+1/2013^2013+1
b=2013^2013+1/2013^2014+1
thực hiện so sánh:
A=20132012+1/20132013+1 với B=20132013+1/20132014+1
A = (2013/2 + 2013/3+2013/4 + ....+2013/2014) : (2013/1+2012/2 +2011/3+...+1/2013)
\(A=\frac{\frac{2013}{2}+\frac{2013}{3}+\frac{2013}{4}+...+\frac{2013}{2014}}{\frac{2013}{1}+\frac{2012}{2}+\frac{2011}{3}+...+\frac{1}{2013}}\)
\(A=\frac{2013.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}\right)}{\left(1+\frac{2012}{2}\right)+\left(1+\frac{2011}{3}\right)+...+\left(1+\frac{1}{2013}\right)+1}\)
\(A=\frac{2013.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}\right)}{\frac{2014}{2}+\frac{2014}{3}+...+\frac{2014}{2013}+\frac{2014}{2014}}\)
\(A=\frac{2013.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}\right)}{2014.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}+\frac{1}{2014}\right)}\)
\(A=\frac{2013}{2014}\)
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\(A=\frac{\frac{2013}{2}+\frac{2013}{3}+\frac{2013}{4}+...+\frac{2013}{2014}}{\frac{2013}{1}+\frac{2012}{2}+\frac{2011}{3}+...+\frac{1}{2013}}\)
\(=\frac{2013.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}\right)}{\left(1+\frac{2012}{2}\right)+\left(1+\frac{2011}{3}\right)+...+\left(1+\frac{1}{2013}\right)+1}\)
\(=\frac{2013.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}\right)}{\frac{2014}{2}+\frac{2014}{3}+...+\frac{2014}{2013}+\frac{2014}{2014}}\)
\(=\frac{2013.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}\right)}{2014.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}+\frac{1}{2014}\right)}\)
\(=\frac{2013}{2014}\)
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so sánh giá trị của A và B với A=2013^2015 -1 / 2013^2016 -1 B=2013^2013 +1 / 2013^2014 +1
2013*x+x*1/2013-2013=1/2013
\(2013.x+x.\frac{1}{2013}-2013=\frac{1}{2013}\)
\(x.\left(2013+\frac{1}{2013}\right)=\frac{1}{2013}+2013\)
\(x=\left(\frac{1}{2013}+2013\right):\left(2013+\frac{1}{2013}\right)\)
\(x=1\)
chúc bạn học tốt
2013 x X + X x 1/2013 - 2013 = 1/2013
Xx(2013+1/2013)=1/2013+2013
X=(1/2013+2013):(1/2013+2013)
X=1
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