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A=2006^2005+1/2006^2006+1
B=2006^2006+1/2006^2007+1
Có : 2006A = 2006^2006+2006/2006^2006+1
= 1 + 2005/2006^2006+1 2006B
= 2006^2007+2006/2006^2007+1
= 1 + 2005/2006^2007+1
Vì : 2006^2006 < 2006^2007
=> 2006^2006+1 < 2006^2007+1
=> 2005/2006^2006+1 > 2005/2006^2007+1
=> 2016A > 2016B
=> A>B
Ta có:
\(A=\frac{2006^{2005}+1}{2006^{2006}+1}\)
\(\Rightarrow2006A=\frac{2006^{2006}+2006}{2006^{2006}+1}=\frac{\left(2006^{2006}+1\right)+2005}{2006^{2006}+1}=1+\frac{2005}{2006^{2006}+1}\)
Ta lại có:
\(B=\frac{2006^{2006}+1}{2006^{2007}+1}\)
\(\Rightarrow2006B=\frac{2006^{2007}+2006}{2006^{2007}+1}=\frac{\left(2006^{2007}+1\right)+2005}{2006^{2007}+1}=1+\frac{2005}{2006^{2007+1}}\)
Ta thấy:
\(\frac{2005}{2006^{2006}+1}>\frac{2005}{2006^{2007}+1}\Rightarrow2006A>2006B\Rightarrow A>B\)
Vậy A>B.
Ai k mình, mình k lại.
B = \(\frac{2001}{2002}+\frac{2002}{2003}\)
có: \(\frac{2000}{2001}>\frac{2000}{2001}+2002\)
\(\frac{2001}{2002}>\frac{2001}{2001}+2002\)
Vậy A>B
\(A=\frac{2006^{2006}+1}{2006^{2007}+1}\) VÀ \(B=\frac{2006^{2005}+1}{2006^{2006}+1}\)
Ta có: \(A=\frac{2006^{2006}+1}{2006^{2007}+1}< 1\)
Nên \(A=\frac{2006^{2006}+1}{2006^{2007}+1}< \frac{2006^{2006}+1+2005}{2006^{2007}+1+2005}=\frac{2006^{2006}+2006}{2006^{2007}+2006}\)
\(=\frac{2006.\left(2006^{2005}+1\right)}{2006.\left(2006^{2006}+1\right)}\)
\(=\frac{2006^{2005}+1}{2006^{2006+1}}=B\)
Vậy \(A< B\)
a,\(A=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2005}-\frac{1}{2006}\)
\(A=\left(1+\frac{1}{3}+...+\frac{1}{2005}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2006}\right)\)
\(A=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2006}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2006}\right)\)
\(=B\left(ĐPCM\right)\)
b, \(A=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2006}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{1003}\right)\)
\(A=\frac{1}{1004}+\frac{1}{1005}+...+\frac{1}{2006}\)
ui ghi lộn, chữ đpcm chuyển xuống dòng cuối cùng nhé :v