A) =(2001+2002+2003)^3

=6006^3

B) =(2004+2005+2006)^3

=6015^3

C) =(2007+2008+2009)

=6024^3

2001³ + 2002³ + 2003³ + 2004³ + 2005³ + 2006³ + 2007³ + 2008³ + 2009³ =  \(\sum\limits^{2009}_{2001}x^3\) = 72541712030

2002/2001>:,2003/2002>1.....

CÓ 8 PHÂN SỐ MỖI PHÂN SỐ CÓ GIÁ TRỊ LỚN HƠN 1 VÂY TỔNG CỦA 8 PHÂN SỐ LỚN HƠN 1 SẼ LỚN HƠN 8.

\(A=\frac{2002}{2001}+\frac{2003}{2002}+\frac{2004}{2003}+\frac{2005}{2004}+\frac{2006}{2005}+\frac{2007}{2006}+\frac{2008}{2007}+\frac{2009}{2008}>\frac{2001}{2001}+\frac{2002}{2002}+\frac{2003}{2003}+\frac{2004}{2004}+\frac{2005}{2005}+\frac{2006}{2006}+\frac{2007}{2007}+\frac{2008}{2008}\)

\(A=\frac{2002}{2001}+\frac{2003}{2002}+\frac{2004}{2003}+\frac{2005}{2004}+\frac{2006}{2005}+\frac{2007}{2006}+\frac{2008}{2007}+\frac{2009}{2008}>1+1+1+1+1+1+1+1\)\(A=\frac{2002}{2001}+\frac{2003}{2002}+\frac{2004}{2003}+\frac{2005}{2004}+\frac{2006}{2005}+\frac{2007}{2006}+\frac{2008}{2007}+\frac{2009}{2008}>8\)

\(A>8\)

A = 2001³ + 2002³ + 2003³ + 2004³ + 2005³ + 2006³ + 2007³ + 2008³ + 2009³

= ( 2001 + 2002 + 2003 + 2004 + 2005 + 2006 + 2007 + 2008 + 2009 )³

= ( ( 2001 + 2009 ) + ( 2002 + 2008 ) + ( 2003 + 2007 )  + ( 2004 + 2006 ) + 2005 )³

= ( 4010 + 4010 + 4010 + 4010 + 2005 ) ³

= ( 4010 . 4 + 2005 )³

= ( 16040 + 2005 )³

= 18045³

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