Tính :
\(\frac{1+\frac{1}{2}+\frac{1}{3}+..........+\frac{1}{2011}+\frac{1}{2012}}{\frac{2013}{1}+\frac{2014}{2}+\frac{2015}{3}+..............+\frac{4023}{2011}+\frac{4024}{2012}}-2012\)
Những câu hỏi liên quan
giải phương trình :
\((1+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{2011}+\frac{1}{2012})503x=1+\frac{2014}{2}+\frac{2015}{3}+...+\frac{4023}{2011}+\frac{4024}{2012}\)
\(\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}\right)\cdot503x=1+\frac{2014}{2}+\frac{2015}{3}+...+\frac{4024}{2012}\)
\(\Leftrightarrow503x=\frac{1+\frac{2014}{2}+\frac{2015}{3}+...+\frac{4024}{2012}}{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}}\)
\(\Leftrightarrow503x=\frac{\frac{2014}{2}-1+\frac{2015}{3}-1+...+\frac{4024}{2012}-1+2012}{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}}\)
\(\Leftrightarrow503x=\frac{\frac{2012}{2}+\frac{2012}{3}+...+\frac{2012}{2012}+2012}{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}}\)
\(\Leftrightarrow503x=\frac{2012\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}\right)}{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}}\)
\(\Leftrightarrow503x=2012\)
\(\Leftrightarrow x=\frac{2012}{503}\)
tìm x biết:
\(\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}+\frac{1}{2012}\right).503x\)\(=\frac{2014}{2}+\frac{2015}{3}+...+\frac{4023}{2011}+\frac{4024}{2012}\)
Xét \( A = 1 + \dfrac{{2014}}{2} + \dfrac{{2015}}{3} + ... + \dfrac{{4023}}{{2011}} + \dfrac{{4024}}{{2012}}\\ \)
\(\Rightarrow A - 2012 = \left( {\dfrac{{2014}}{2} - 1} \right) + \left( {\dfrac{{2015}}{3} - 1} \right) + ... + \left( {\dfrac{{4024}}{{2012}} - 1} \right)\\ \Rightarrow A - 2012 = \dfrac{{2012}}{2} + \dfrac{{2012}}{3} + ... + \dfrac{{2012}}{{2012}}\\ \Rightarrow A - 2012 = 2012\left( {\dfrac{1}{2} + \dfrac{1}{3} + ... + \dfrac{1}{{2012}}} \right)\\ \Rightarrow A = 2012\left( {1 + \dfrac{1}{2} + ... + \dfrac{1}{{2012}}} \right)\\ \Rightarrow \left( {1 + \dfrac{1}{2} + \dfrac{1}{3} + ... + \dfrac{1}{{2012}}} \right)503x = 2012\left( {1 + ... + \dfrac{1}{{2012}}} \right)\\ \Rightarrow x = \dfrac{{2012}}{{503}} = 4 \)
Giải phương trình sau ( giải từng bước nhá các bạn )
a) ( 1 + 1/2 + 1/3 + ..... + 1/2011 + 1/2012 ) . 503x = 1 + 2014/2 + 2015/3 + ...... + 4023/2011 + 4024/2012
c) ( \(\frac{2011}{1\cdot11}\) + \(\frac{2012}{2\cdot12}+.....+\frac{2011}{100\cdot110}\) ) x = \(\frac{2011}{1\cdot110}+\frac{2011}{2\cdot102}+....+\frac{2011}{10\cdot110}\)
từng bước bao gồm cả lập luân luôn
a)\(\left(1+\frac{1}{2}+...+\frac{1}{2012}\right).503x=1+\frac{2014}{2}+\frac{2015}{3}+...+\frac{4023}{2011}+\frac{4024}{2012}\) (1)
\(A=\frac{2014}{2}+\frac{2015}{3}+...+\frac{4023}{2011}+\frac{4024}{2012}\) (có 2011 số hạng)
nếu ta trừ một vào từng số hạng được tử số giống nhau
\(A-2011=\left(\frac{2014}{2}-1\right)+\left(\frac{2015}{3}-1\right)+...+\left(\frac{4023}{2011}-1\right)+\left(\frac{4024}{2012}-1\right)\)
\(A-2011=\frac{2012}{2}+\frac{2012}{3}+...+\frac{2012}{2011}+\frac{2012}{2012}=2012\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}+\frac{1}{2012}\right)\)
\(A-2011+2012=2012\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}+\frac{1}{2012}\right)\)công 2012 hai vế
\(A+1=VP=2012\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}+\frac{1}{2012}\right)\)
\(\left(1\right)\Leftrightarrow\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}+\frac{1}{2012}\right).503x=2012\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}+\frac{1}{2012}\right)\left(2\right)\)
Chia cả hai vế (2) cho: \(\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}+\frac{1}{2012}\right)\Rightarrow503x=2012\)
\(x=\frac{2012}{503}\)
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GPT :a, left(1+frac{1}{2}+frac{1}{3}+...+frac{1}{2011}+frac{1}{2012}..right).503x1+frac{2014}{2}+frac{2015}{3}+...+frac{4023}{2011}+frac{4024}{2012}b, left(frac{0,6+frac{3}{7}-frac{2}{11}}{1+frac{5}{7}-frac{5}{11}}+frac{frac{2}{3}-1,5+frac{2}{9}}{frac{5}{3}-3,75+frac{5}{9}}right)+93xleft(frac{3737}{4545}-frac{954954}{975975}right).left(frac{1}{2}-frac{1}{3}-frac{1}{6}right)-7.left(x-3right)
Đọc tiếp
GPT :
a, \(\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}+\frac{1}{2012}..\right).503x=1+\frac{2014}{2}+\frac{2015}{3}+...+\frac{4023}{2011}+\frac{4024}{2012}\)
b, \(\left(\frac{0,6+\frac{3}{7}-\frac{2}{11}}{1+\frac{5}{7}-\frac{5}{11}}+\frac{\frac{2}{3}-1,5+\frac{2}{9}}{\frac{5}{3}-3,75+\frac{5}{9}}\right)+93x=\left(\frac{3737}{4545}-\frac{954954}{975975}\right).\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)-7.\left(x-3\right)\)
\(VP=1+\frac{2014}{2}+\frac{2015}{3}+...+\frac{4023}{2011}+\frac{4024}{2012}\)
\(=1-1+\left(\frac{2014}{2}-1\right)+\left(\frac{2015}{3}-1\right)+...+\left(\frac{4023}{2011}-1\right)+\left(\frac{40024}{2012}-1\right)+2012\)
\(=\frac{2012}{2}+\frac{2012}{3}+...+\frac{2012}{2011}+\frac{2012}{2012}+\frac{2012}{1}\)
\(=2012.\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}+\frac{1}{2012}\right)\)
\(\Rightarrow2012=503.x\Rightarrow x=\frac{2012}{503}=4\)
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GPT :
a, left(1+frac{1}{2}+frac{1}{3}+...+frac{1}{2011}+frac{1}{2012}..right).503x1+frac{2014}{2}+frac{2015}{3}+...+frac{4023}{2011}+frac{4024}{2012}
b, left(frac{0,6+frac{3}{7}-frac{2}{11}}{1+frac{5}{7}-frac{5}{11}}+frac{frac{2}{3}-1,5+frac{2}{9}}{frac{5}{3}-3,75+frac{5}{9}}right)+93xleft(frac{3737}{4545}-frac{954954}{975975}right).left(frac{1}{2}-frac{1}{3}-frac{1}{6}right)-7.left(x-3right)
Đọc tiếp
GPT :
a, \(\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}+\frac{1}{2012}..\right).503x=1+\frac{2014}{2}+\frac{2015}{3}+...+\frac{4023}{2011}+\frac{4024}{2012}\)
b, \(\left(\frac{0,6+\frac{3}{7}-\frac{2}{11}}{1+\frac{5}{7}-\frac{5}{11}}+\frac{\frac{2}{3}-1,5+\frac{2}{9}}{\frac{5}{3}-3,75+\frac{5}{9}}\right)+93x=\left(\frac{3737}{4545}-\frac{954954}{975975}\right).\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)-7.\left(x-3\right)\)
\(\frac{1+\frac{1}{2}+\frac{1}{3}+....\frac{1}{2012}}{\frac{2013}{1}+\frac{2014}{2}+\frac{2015}{3}....\frac{4024}{2012}-2012}\)
tính nhanh cả nhà ơi
\(\frac{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}}{\frac{2013}{1}+\frac{2014}{2}+\frac{2015}{3}+...+\frac{4024}{2012}-2012}\)
\(=\frac{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}}{\left(\frac{2013}{1}-1\right)+\left(\frac{2014}{2}-1\right)+\left(\frac{2015}{3}-1\right)+...+\left(\frac{4024}{2012}-1\right)}\)
\(=\frac{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}}{\frac{2012}{1}+\frac{2012}{2}+\frac{2012}{3}+...+\frac{2012}{2012}}\)
\(=\frac{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}}{2012.\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}\right)}\)
\(=\frac{1}{2012}\)
Ủng hộ mk nha ^_-
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Không tính cụ thể , hãy sắp xếp các biểu thức sau theo thứ tự giảm dần :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{2011}{2012}+frac{2012}{2013}}{frac{2012}{2013}+frac{2013}{2014}+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...
Đọc tiếp
Không tính cụ thể , hãy sắp xếp các biểu thức sau theo thứ tự giảm dần :
\(\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}\)
\(\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}\)
\(\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012+2013+2014}{2013+2014+2015}}\)
\(\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012+2013+2014}{2013+2014+2015}}\)
\(\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}\)
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}$
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Xem thêm câu trả lời
frac{frac{1}{2}+frac{1}{3}+......+frac{1}{2013}}{frac{2012}{1}+frac{2012}{2}+frac{2011}{3}+...+frac{1}{2013}}frac{frac{1}{2}+frac{1}{3}+..+frac{1}{2013}}{frac{2012}{1}+2+frac{2012}{2}+1+frac{2011}{3}+1+...+frac{1}{2013}+1-2014}frac{frac{1}{2}+frac{1}{3}+...+frac{1}{2013}}{frac{2014}{1}+frac{2014}{2}+...+frac{2014}{2013}-2014}frac{frac{1}{2}+frac{1}{3}+...+frac{1}{2013}}{2014left(1+frac{1}{2}+frac{1}{3}+...+frac{1}{2013}-1right)}frac{1}{2014}
Đọc tiếp
\(\frac{\frac{1}{2}+\frac{1}{3}+......+\frac{1}{2013}}{\frac{2012}{1}+\frac{2012}{2}+\frac{2011}{3}+...+\frac{1}{2013}}\)
=\(\frac{\frac{1}{2}+\frac{1}{3}+..+\frac{1}{2013}}{\frac{2012}{1}+2+\frac{2012}{2}+1+\frac{2011}{3}+1+...+\frac{1}{2013}+1-2014}\)
=\(\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}}{\frac{2014}{1}+\frac{2014}{2}+...+\frac{2014}{2013}-2014}\)
=\(\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}}{2014\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}-1\right)}\)
=\(\frac{1}{2014}\)
Tính giá trị biểu thức :
\(A=\frac{\frac{1}{2013}+\frac{2}{2012}+\frac{3}{2011}+...+\frac{2011}{3}+\frac{2012}{2}+\frac{2013}{1}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{2012}+\frac{1}{2013}+\frac{1}{2014}}\)
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