A= 1.2+2.3+3.4+...+2015.2016

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

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

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

    =2015.2016.2017

A=2015.2016.2017:3=2731179360

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

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

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

3A = 2014.2015.2016

A = 2727117120

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{2016.2017}\)

\(A=\left(\frac{1}{1}-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+......+\left(\frac{1}{2016}-\frac{1}{2017}\right)\)

\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{2016}-\frac{1}{2017}\)

\(A=\frac{1}{1}-\frac{1}{2017}\)

\(A=\frac{2016}{2017}\)

A=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{2016.2017}\)

\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+......+\frac{1}{2016}-\frac{1}{2017}\)

\(\Rightarrow A=1-\frac{1}{2017}\)

\(\Rightarrow A=\frac{2016}{2017}\)

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2015.2016}+\frac{1}{2016.2017}\)

\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{2015}-\frac{1}{2016}+\frac{1}{2016}-\frac{1}{2017}\)

\(\Rightarrow A=1-\frac{1}{2017}\)

\(\Rightarrow A=\frac{2016}{2017}\)

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

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 = \(\frac{2015.2016.2017}{3}\)

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

=> A=\(\frac{2015.2016.2017}{3}=2731179360\)

.

.

Đặt \(A=1.2+2.3+3.4+...+2015.2016\)

\(\Rightarrow3A=1.2.3+2.3.3+3.4.3+...+2015.2016.3\)

\(\Rightarrow3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+2015.2016.\left(2017-2014\right)\)

\(\Rightarrow3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+2015.2016.2017-2014.2015.2016\)

\(\Rightarrow3A=2015.2016.2017\)

\(\Rightarrow A=2015.2016.2017:3\)

\(\Rightarrow A=2015.672.2017\)

Vậy \(A=2015.672.2017\)

1 . 2 + 2 . 3 + 3 . 4 + ... + 2015 . 2016

3M = 1 . 2 . 3 + 2 . 3 . 3 + 3 . 4 . 3 + ... + 2015 . 2016 . 3 

3M = 1 . 2 ( 3 - 0 ) + 2 . 3 ( 4 - 1 ) + 3 . 4 ( 5 - 2 ) + ... + 2015 . 2016 ( 2017 - 2014 )

3M = ( 1 . 2 . 3 + 2 . 3 . 4 + 3 . 4. 5 + ... + 2015 . 2016 . 2017 ) - ( 0 . 1 . 2 + 1 . 2 . 3 + 2 . 3 . 4 + ... + 2014 . 2015 . 2016 )

3M = 2015 . 2016 . 2017

M = \(\frac{2015.2016.2017}{3}\)

M = 2731179360

Gọi tổng 1.2+2.3+3.4+...+2015.2016 là M

\(\text{M = 1.2+2.3+3.4+...+2015.2016}\)

\(3M=1.2.3+2.3.3+3.4.3+...+2015.2016.3\)

\(3M=1.2\left(3-0\right)+2.3\left(4-1\right)+3.4\left(5-2\right)+...+2015.2016.\left(2017-2014\right)\)

\(3M=\left(1.2.3+2.3.4+3.4.5+...+2015.2016.2017\right)-\left(0.1.2+1.2.3+2.3.4+...+2014.2015.2016\right)\)

\(M=2015.2016.2017\)

\(M=\frac{2015.2016.2017}{3}\)

\(M=672.2015.2017\)

\(M=2731179360\)