Question

tính M= 1.2+2.3+3.4+...+2002.2003 bàng bao nhiêu???

Answer 1

\(M=1.2+2.3+3.4+...+2002.2003\)

\(3.M=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+2002.2003.\left(2004-2001\right)\)

\(3.M=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...-...+2002.2003.2004-2001.2002.2003\)

\(3.M=2002.2003.2004\)

\(M=2002.2003.2004:3=2002.2003.668\)

\(M=2678684008\)

Answer 2

M = 1 . 2 + 2 . 3 + 3 . 4 + ... + 2002 . 2003

3M = 1 . 2 . 3 + 2 . 3 . 4 + 3 . 4 . 3 + ... + 2002 . 2003 . 3

3M = 1 . 2 ( 4  - 1 ) + 2 . 4 ( 5 - 2 ) + 3 . 4 ( 6 - 3 ) + ... + 2002 . 2003 ( 2005 - 2002 )

3M = 1 . 2 . 3 + 2 . 3 . 4 - 1 . 2 . 3 + 3 . 4 . 5 - 2 . 3 . 4 + .... - 2002 . 2003 . 2004 + 2004 . 2005 . 2006

3M = 2005 . 2006 . 2007

3M = 2005 . 2006 . 889 . 3

M = 2005 . 2006 . 889

M = 4022030