Question

\(tinh:m+1\cdot2+2\cdot3+...+2012\cdot2013\)

ai tra loi nhanh nhat mik tich cho

Answer 1

Ta có : M = 1.2 + 2.3 + 3.4 + ...... + 2012.2013

 => 3M = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ...... + 2012.2013.2014

=> 3M = 2012.2013.2014

=> M = 2012.2013.2014/3

=> M = 2719004728

Answer 2

M = 1.2 + 2.3 + ..... + 2012.2013

3M = 1.2.3 + 2.3.3 + .... + 2012.2013.3

= 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + .... + 2012.2013.(2014 - 2011)

= 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + .... + 2012.2013.2014 - 2011.2012.2013

= 2012.2013.2014

\(\Rightarrow M=\frac{2012.2013.2014}{3}\)