Question

Tính tổng của A=1.2+2.3+3.4+...+2015.2016.

Answer 1

A= 1.2+2.3+3.4+...+2015.2016

3A=1.2.3+2.3.3+3.4.3+...+2015.2016.3

3A=1.2.3+2.3.(4-1)+3.4.(5-2)+...+2015.2016.(2017-2014)

3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+2015.2016.2017-2014.2015.2016

3A=2015.2016.2017

3A=8193538080

A=8193538080:3

A=2731179360

Answer 2

3A = 1.2.3 + 2.3.3 + 3.4.3 + ..... + 2015.2016.3

=> 3A = 1.2.3 + 2.3.( 4 -1 ) + 3.4.( 5 - 2 ) + .... + 2015.2016.( 2017 - 2014 )

=> 3A = 1.2.3 + 2.3.4 - 1.2.3 + .... + 2015.2016.2017 - 2014.2015.2016

=> 3A = 2015.2016.2017

=> A = \(\frac{2015.2016.2017}{3}\)