\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2011}}{\frac{2010}{1}+\frac{2009}{2}+\frac{2008}{3}+...+\frac{1}{2010}}\)

\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+..+\frac{1}{2011}}{\left(\frac{2009}{2}+1\right)+\left(\frac{2008}{3}+1\right)+...+\left(\frac{1}{2010}+1\right)+1}\)

\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2011}}{\frac{2011}{2}+\frac{2011}{3}+...+\frac{2011}{2010}+\frac{2011}{2011}}\)

\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2011}}{2011\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2010}+\frac{1}{2011}\right)}\)

\(A=\frac{1}{2011}\)

dunt

Gọi \(S=\frac{2009}{1}+\frac{2008}{2}+...+\frac{1}{2009}\)

\(\Rightarrow S=\frac{2010-1}{1}+\frac{2010-2}{2}+...+\frac{2010-2009}{2009}\)

\(\Rightarrow S=2010-1+\frac{2010}{2}-1+...+\frac{2010}{2009}-1\)

\(\Rightarrow S=2010+\frac{2010}{2}+...+\frac{2010}{2009}-\left(1+1+..+1\right)\)

\(\Rightarrow S=2010+\frac{2010}{2}+...+\frac{2010}{2009}-2009\)

\(\Rightarrow S=\frac{2010}{2}+\frac{2010}{3}+...+\frac{2010}{2009}+1\)

\(\Rightarrow S=\frac{2010}{2}+\frac{2010}{3}+..+\frac{2010}{2009}+\frac{2010}{2010}\)

\(\Rightarrow S=2010\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2010}\right)\)

Khi đó \(A=\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2010}}{2010\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2010}\right)}=\frac{1}{2010}\)

a) A= 1/2010+1+2/2009+1+3/2008+1+...+2009/2+1+1

  = 2011/2010+20011/2009+2011/2008+...+2011/2+2011/2011

  = 2011(1/2+1/3+1/4+...+1/2011)

Ta có: B= 1/2+1/3+1/4+...+1/2011

suy ra A/B= 2011

=1/2010

\(\frac{A}{B}\)=2011

Ta có: A=\(\frac{1}{2011}+\frac{2}{2010}+\frac{3}{2009}+...+\frac{2009}{3}+\frac{2010}{2}+\frac{2011}{1}\)

=> A=\(\frac{2012-2011}{2011}+\frac{2012-2010}{2010}+...+\frac{2012-2}{2}+\frac{2012-1}{1}\)

=>A=\(\frac{2012}{2011}-1+\frac{2012}{2010}-1+...+\frac{2012}{2}-1+2012-1\)

=>A=\(2012\cdot\left(\frac{1}{2011}+\frac{1}{2010}+...+\frac{1}{2}\right)+1\)

=> A= \(2012\cdot\left(\frac{1}{2012}+\frac{1}{2011}+...+\frac{1}{2}\right)\)

ko biết có đúng hay ko nựa sai thì bỏ qua nha ^^

dung r bn oi

con co cau p=1/2+1/3+...+1/2011+1/2012

\(C=\frac{\frac{1}{2008}-\frac{1}{2009}-\frac{1}{2010}}{\frac{5}{2008}-\frac{5}{2009}-\frac{5}{2010}}+\frac{\frac{2}{2007}-\frac{2}{2008}-\frac{2}{2009}}{\frac{3}{2007}-\frac{3}{2008}-\frac{3}{2009}}\)

\(=\frac{\frac{1}{2008}-\frac{1}{2009}-\frac{1}{2010}}{5.\left(\frac{1}{2008}-\frac{1}{2009}-\frac{1}{2010}\right)}+\frac{2.\left(\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2009}\right)}{3.\left(\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2009}\right)}\)

\(=\frac{1}{5}+\frac{2}{3}\)

\(=\frac{13}{15}\)

Ghi lộn đề thiếu thì phải. Hình như thiếu phân số 1/2011

\(A=\frac{2010}{1}+\frac{2009}{2}+...+\frac{2}{2009}+\frac{1}{2010}\)

\(A=1+\left(\frac{2009}{2}+1\right)+...+\left(\frac{2}{2009}+1\right)+\left(\frac{1}{2010}+1\right)\)

\(A=\frac{2011}{2011}+\frac{2011}{2}+...+\frac{2011}{2009}+\frac{2011}{2010}\)

\(A=\frac{2011}{2}+...+\frac{2011}{9}+\frac{2011}{10}+\frac{2011}{11}\)

\(A=2011.\left(\frac{1}{2}+...+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}\right)\)

\(A=2011.B\)

Nên : \(\frac{A}{B}=\frac{2011.B}{B}=2011\)

Vậy \(\frac{A}{B}=2011\)

Tham khảo nha !!! Chúc bạn học tốt !!! 

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Ta có: \(C=\frac{\frac{2010}{1}+\frac{2009}{2}+\frac{2008}{3}+...+\frac{1}{2010}}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}}\)

Đặt \(A=\frac{2010}{1}+\frac{2009}{2}+\frac{2008}{3}+...+\frac{1}{2010}\)

\(A=\frac{2010}{1}+1+\frac{2009}{1}+1+\frac{2008}{1}+1+...+\frac{1}{2010}+1-2010\)

\(=\frac{2011}{1}+\frac{2011}{2}+\frac{2011}{3}+...+\frac{2011}{2010}-\frac{2011.2010}{2011}\)

\(=2011\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2010}-\frac{2010}{2011}\right)\)

Đặt \(B=\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}\)

\(B=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}-1\)

\(=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2010}-\frac{2010}{2011}\)

Ta có: \(C=\frac{A}{B}=2011\)(lấy A-B)

Ta có :

\(2010A=\dfrac{2010^{2012}+2010}{2010^{2012}+1}=\dfrac{2010^{2012}+1+2009}{2010^{2012}+1}=1+\dfrac{2009}{2010^{2012}+1}\)

\(2010B=\dfrac{2010^{2011}+2010}{2010^{2011}+1}=\dfrac{2010^{2011}+1+2009}{2010^{2011}+1}=1+\dfrac{2009}{2010^{2011}+1}\)

Vì \(1+\dfrac{2009}{2010^{2012}+1}< 1+\dfrac{2009}{2010^{2011}+1}\Rightarrow A< B\)

~ Học tốt ~

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