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\(A=\frac{2012.2010+2013}{2011.2011+2012}\)
\(\Rightarrow A=\frac{\left(2011+1\right).\left(2011-1\right)+2013}{2011.2011+2012}\)
\(\Rightarrow A=\frac{2011\left(2011+1\right)-2011-1+2013}{2011.2011+2012}\)
\(\Rightarrow A=\frac{2011^2+2011-2011-1+2013}{2011^2+2012}\)
\(\Rightarrow A=\frac{2011^2-1+2013}{2011^2+2012}\)
\(\Rightarrow A=\frac{2011^2+2012}{2011^2+2012}=1\)
Vậy A = 1
\(\frac{A}{B}=\frac{2010+2011\times2012}{2012\times2013-2014}\)
B = 2012 x 2013 - 2014 = 2012 x (2011+2) - 2014 = 2012 x 2011 + 2012 x 2 - 2014 = 2012 x 2011 + 2010 = 2010 + 2011 x 2012
Thay B vào biểu thức tính thương, ta được:
\(\frac{A}{B}=1\)
Đáp số: 1
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Bài giải
Ta có:
2010 + 2011 x 2012 /2012 x 2013 – 2014
= ( 2010 + 2011 x 2012) / (2012 x (2011 + 2) – 2014)
= ( 2010 + 2011 x 2012) / (2012 x 2011) + ((2012 x2 ) – 2014)
= ( 2010 + 2011 x 2012) / (2012 x 2011) + 2010
= 1/1
= 1
nhin vao de la bik = 1 rui ko can phai lam dai dong vay dau
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}$
a)
Ta có a > b vì b > 3 còn a < 3
b)
a. Ta có : 1/51 + 1/52 + 1/53 +...+ 1/60 < 1/51 x 10 < 1/50 x 10 = 1/5
=> 1/51 + 1/52 +1/53 +...+1/60 < 1/5
b. Ta có : 1/51 + 1/52 + 1/53 +...+ 1/60 > 1/60 x 10 = 1/6
=> 1/51 + 1/52 +1/53 +...+ 1/60 > 1/6
a. 1⋅2⋅3+2⋅4⋅6+3⋅6⋅9+4⋅8⋅12
= 6+2⋅4⋅6+3⋅6⋅9+4⋅8⋅12
= 6+48+3⋅6⋅9+4⋅8⋅12
= 6+48+162+4⋅8⋅12
= 6+48+162+384
= 600
b . Ta có \(A=\frac{2010+2011}{2011+2012}=\frac{2010}{2011+2012}+\frac{2011}{2011+2012}.\)
Ta có : \(\frac{2010}{2011+2012}< \frac{2010}{2011}\) và \(\frac{2011}{2011+2012}< \frac{2011}{2012}\)
=> \(\frac{2010+2011}{2011+2012}< \frac{2010}{2011}+\frac{2011}{2012}\)
=> A < B
\(\dfrac{2012x2010+2011}{2010x2013+1}=\dfrac{4044120+2011}{4046130+1}=\dfrac{4046131}{4046131}\)\(=1\)
2012 x 2010 + 2011 phần 2010 x 2013 + 1=1