Tính giá trị biểu thức:
a)242,4:10-(242,4x0,09+242,4x0,01)
b)20,12x0,082-2011:1000+20,12x0,018
Giúp mik nha mấy bn!
Thanks mn nhiều!
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\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}}{\frac{2013}{1}+\frac{2012}{2}+\frac{2011}{3}+...+\frac{1}{2013}}\)
\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}}{\left(\frac{2012}{2}+1\right)+\left(\frac{2011}{3}+1\right)+...+\left(\frac{1}{2013}+1\right)+1}\)
\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}}{\frac{2014}{2}+\frac{2014}{3}+...+\frac{2014}{2013}+\frac{2014}{2014}}\)
\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}}{2014.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}\right)}\)\
\(A=\frac{1}{2014}\)
\(A=-\frac{9}{10^{2012}}+-\frac{19}{10^{2011}}=-\frac{9}{10^{2012}}+-\frac{9}{10^{2011}}+-\frac{10}{10^{2011}}\)
\(B=-\frac{9}{10^{2011}}+-\frac{19}{10^{2012}}=-\frac{9}{10^{2011}}+-\frac{9}{10^{2012}}+-\frac{10}{10^{2012}}\)
Mà \(-\frac{9}{10^{2012}}=-\frac{9}{10^{2012}};-\frac{9}{10^{2011}}=-\frac{9}{10^{2011}};-\frac{10}{10^{2012}}>-\frac{10}{10^{2011}}\)
\(\Rightarrow-\frac{9}{10^{2011}}+-\frac{9}{10^{2012}}+-\frac{10}{10^{2012}}>-\frac{9}{10^{2011}}+-\frac{9}{10^{2012}}+-\frac{10}{10^{2011}}\)
\(\Rightarrow B>A\)
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Siêu tốc tổng quát: \(\frac{1}{n.\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)áp vào
\(A=\frac{1}{1}-\frac{1}{14}=1-\frac{1}{14}\)
A=(2-1)/1.2+(3-2)/2.3+...+(14-13)/13.14
A=1-1/2+1/2-1/3+...+1/13-1/14
A=1-1/14=13/14
\(A=\frac{\frac{2}{3}+\frac{2}{5}-\frac{2}{9}}{\frac{4}{3}+\frac{4}{5}-\frac{4}{9}}\) \(\Leftrightarrow A=2\left(\frac{1}{3}+\frac{1}{5}-\frac{1}{9}\right).\frac{1}{4}\left(\frac{1}{3}+\frac{1}{5}-\frac{1}{9}\right)\)
\(\Leftrightarrow A=\frac{1}{2}\)
Là câu C.
Nếu làm trắc nghiệm thì bấm máy tính cho nhanh.
a) \(A=\left(-10\right)+\left(-34\right)+\left(-26\right)\)
\(=\left(-10\right)+\left[\left(-34\right)+\left(-26\right)\right]\)
\(=\left(-10\right)+\left(-60\right)\)
\(=-70\)
\(A=3\left|1-2x\right|-5\)
Ta có: \(\left|1-2x\right|\ge0\forall x\)
\(\Rightarrow3.\left|1-2x\right|-5\ge-5\forall x\)
\(\Rightarrow A\ge-5\forall x\)
Dấu "=" xảy ra
\(\Leftrightarrow3.\left|1-2x\right|=0\Leftrightarrow1-2x=0\Leftrightarrow x=\dfrac{1}{2}\)
a) 242,4 : 10 - ( 242,4 x 0,09 + 242,4 x0 ,01 )
=242,4 : 10 - [ 242,4 x ( 0,09 +0 ,01 ) ]
=242,4 : 10 - 242,4 x 0,1
=242,4 : 10 - 242,4 : 10
=0
b) 20,12 x 0,082 - 2011 : 1000 + 20,12 x 0,018
=20,12 x ( 0,082 + 0,018 ) - 2011 : 1000
=20,12 x 0,01 - 2011 : 1000
=20,12 : 100 - 2011 : 1000
=0,2012 - 0,2011
=0,0001