A = 1X2 +2x3 +...+ 2016x2107

3A = 1x2x3 + 2x3x3 + ...+ 2016x2017x3

3A = 1x2x(3-0) + 2x3x(4-1) + ... + 2016x2017x(2018-1)

3A = 1x2x3 - 1x2x0 +2x3x4 -1x2x3 +...+ 2016x2017x2018 - 2016x2017x2015

Ta loại trừ còn

3A = 2016x2017x2018 - 1x2x0

3A = 2016x2017x2018

A = 2016 x2017 x2018 : 3

A = 1x2 +2x3 +3x4 +...+ 2016 x 2017

3A = 1x2x3 + 2x3x3 +...+2016 x 2017 x3

3A = 1x2x(3-0) + 2x3x(4-1) +...+ 2016x2017x(2018-2015)

sửa đề \(C=\frac{3}{1.2}+\frac{3}{2.3}+\frac{3}{3.4}+...+\frac{3}{2015.2016}\)

\(=3\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2015}-\frac{1}{2016}\right)\)

\(=3\left(1-\frac{1}{2016}\right)=3.\frac{2015}{2016}=\frac{2015}{672}\)

\(\frac{1}{1\times2}+\frac{1}{2\times3}+.......+\frac{1}{2015\times2016}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.........+\frac{1}{2015}-\frac{1}{2016}\)

\(=1-\frac{1}{2016}\)

\(=\frac{2015}{2016}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2015}-\frac{1}{2016}\)

\(=\frac{1}{1}-\frac{1}{2016}\)

\(=\frac{2015}{2016}\)

\(B=1.2+2.3+3.4+...+18.19\)

\(3B=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+18.19.\left(20-17\right)\)

\(3B=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+18.19.20-17.18.19\)

\(3B=18.19.20\Rightarrow B=\frac{18.19.20}{3}=2280\)

Ta có :   B = 1 x 2 + 2 x 3 + 3 x 4 +.... + 18 x 19

=> 3B = 1 x 2 x 3 + 2 x 3 x 3 + 3 x 4 x 3 + ... + 18 x 19 x 3

     3B = 1 x 2 x 3 + 2 x 3 x (4 - 1) + 3 x 4 x (5 - 2) + .... + 18 x 19 x (20 - 17)

     3B = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x3 + 3 x 4 x5 - 2 x 3 x 4 + ... + 18 x 19 x 20 - 17 x 18 x 19

     3B = 18 x 19 x 20

       B = 18 x 19 x 20 : 3 

          = 2280

Vậy B = 2280 

nhân 3 lên rồi tính

Đặt \(A=1.2+2.3+...+59.60\)

\(\Rightarrow3A=1.2.3+2.3.\left(4-1\right)+...+59.60.\left(61-58\right)\)

\(\Rightarrow3A=1.2.3+2.3.4-1.2.3+...+59.60.61-58.59.60\)

\(\Rightarrow3A=59.60.61\)

\(\Rightarrow A=\frac{59.60.61}{3}\)

Đặt A = 1×2 + 2×3 + 3×4 + ... + 19×20

⇒ 3A = 1×2×3 + 2×3×3 + 3×4×3 + ... + 19×20×3

= 1×2×3 + 2×3×(4 - 1) + 3×4×(5 - 2) + ... + 19×20×(21 - 18)

= 1×2×3 - 1×2×3 + 2×3×4 - 2×3×4 + 3×4×5 - ... - 18×19×20 + 19×20×21

= 19×20×21

= 7980

⇒ A = 7980 : 3 = 2660

A = 1.2 + 2.3 + .... + 999.1000

3A = 1.2.3 + 2.3.(4-1) + .... + 999.1000.(1001 - 998)

3A = 1.2.3 + 2.3.4 - 1.2,3 +..... + 999.1000.1001 - 998.999.1000

3A = 999 . 1000 . 1001

A = 333 x 1000 x 1001 = 333 333 000

3A=1x2x3+2x3x(4-1)+3x4x(5-2)+.............+999x1000x(1001-998)

3A=1x2x3+2x3x4-1x2x3+3x4x5-2x3x4+............+999x1000x1001-998x999x1000

3A=999x1000x1001

A=999x1000x1001:3

A=333333000

s=2-1+3-2+...+39-38+40-39

  =40-1

 = 39

thank you