Question

Tìm tổng sau:A=1.2+2.3+3.4+...+2014.2015

Answer 1

A=1.2+2.3+....+2014.2015

=>3A=1.2.3+2.3.3+3.4.3+...+2015.2014.3

=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...+2014.2015.(2016-2013)

=1.2.3-0.1.2+2.3.4-1.2.3+3.4.5-2.3.4+4.5.6-3.4.5+.....+2014.2015.2016-2013.2014.2015

=(1.2.3-1.2.3)+(2.3.4-2.3.4)+(3.4.5-3.4.5)+....+(2013.2014.2015-2013.2014.2015)+0.1.2+2013.2014.2015

=0+2013.2014.2015

=>A=\(\frac{2013.2014.2015}{3}\)