Làm theo cách này nhé :
a = 2 / 60 x 63 + 2 / 63 x 66 + 2 / 66x 69 + ...+ 2 / 117 x 120 + 2 / 2011
= 2/3 x ( 3/60 x 63 + 3 / 63 x 66 + 3 / 66 x 69 + ...+ 3/117 x 120 ) + 2/2011
= 2/3 x ( 1/60 - 1/63 + 1/63 - 1/66 + 1/66 - 1/69 + ... + 1/117 - 1/120 ) + 2/2011
= 2/3 x ( 1/60 - 1/120 ) + 2/2011
= 2/3 x 1/120 + 2/2011
= 1/180 + 2/2011
b = 5/ 40 x 44 + 5 / 44 x 48 + ...+ 5/76 x 80 + 5/ 2011
= 5/4 x ( 4/40 x 44 + 4/44 x 48 + ...+ 4/76 x 80 ) + 5/2011
= 5/4 x ( 1/40 - 1/44 + 1/44 - 1/48 + ...+ 1/76 - 1/80 ) + 5/2011
= 5/4 x ( 1/40 - 1/80 ) + 5/2011
= 5/4 x 1/80 + 5/2011
= 1/64 + 5/2011
Do 1/64 > 1/80 ; 5/2011 > 2/2011
=> 1/64 + 5/2011 > 1/80 + 2/2011
=> b > a
K nha
Mình sửa lại chút nhé , lỗi đánh bàn phím thoy , :
Do 1/64 > 1/180 ; 5/2011 > 2/2011
=> 1/64 + 5/2011 > 1/180 + 2/2011
=> b > a
\(A=2\left(\frac{1}{60.63}+\frac{1}{63.66}+..+\frac{1}{117.120}\right)+\frac{2}{2011}\)
\(\Rightarrow3A=2\left(\frac{3}{60.63}+\frac{3}{63.66}+....+\frac{3}{117.120}\right)+\frac{6}{2011}\)
\(\Rightarrow3A=2\left(\frac{1}{60}-\frac{1}{63}+\frac{1}{63}-\frac{1}{66}+...+\frac{1}{117}-\frac{1}{120}\right)+\frac{6}{2011}\)
\(\Rightarrow3A=2\left(\frac{1}{60}-\frac{1}{120}\right)+\frac{6}{2011}\)
\(\Rightarrow\) \(3A=\frac{1}{60}+\frac{6}{2011}\)
\(\Rightarrow A=\frac{1}{60}:3+\frac{6}{2011}:3\)
\(\Rightarrow A=\frac{1}{180}+\frac{2}{2011}\)
\(\Rightarrow B=5\left(\frac{1}{40.44}+\frac{1}{44.48}+..+\frac{1}{76.80}\right)+\frac{5}{2011}\)
\(\Rightarrow4B=5\left(\frac{4}{40.44}+\frac{4}{44.48}+...+\frac{4}{76.80}\right)+\frac{20}{2011}\)
\(\Rightarrow4B=5.\left(\frac{1}{40}-\frac{1}{44}+\frac{1}{44}-\frac{1}{48}+...+\frac{1}{76}-\frac{1}{80}\right)+\frac{20}{2011}\)
\(\Rightarrow4B=5\left(\frac{1}{40}-\frac{1}{80}\right)+\frac{20}{2011}\)
\(\Rightarrow4B=\frac{1}{16}+\frac{20}{2011}\)
\(\Rightarrow B=\frac{1}{16}:4+\frac{20}{2011}:4\)
\(\Rightarrow B=\)\(\frac{1}{64}+\frac{5}{2011}\)
Ta thấy \(\frac{1}{80}< \frac{1}{64}\)
\(\frac{2}{2011}< \frac{5}{2011}\)
\(\Rightarrow\frac{1}{80}+\frac{2}{2011}< \frac{1}{64}+\frac{5}{2011}\)
Hay A<B
