Question

\(1\times2+2\times3+3\times4+4\times5+......+2011\times2012\)

Answer 1

Đặt A = 1 x 2 + 2 x 3 + ... + 2011 x 2012

   3A = 1 x 2 x 3 + 2 x 3 x 3 + ... + 2010 x 2011 x 3 + 2011 x 2012 x 3

   3A = 1 x 2 x 3 + 2 x 3 x (4 - 1) + ... + 2010 x 2011 x (2012 - 2009) + 2011 x 2012 x (2013 - 2010)

   3A = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + ... + 2010 x 2011 x 2012 - 2009 x 2010 x 2011 + 2011 x 2012 x 2013 - 2010 x 2011 x 2012

   3A = 2011 x 2012 x  2013

   3A = 8 144 863 176

     A = 2 714 954 572