Question

1*2+2*3+3*4+4*5+......+9*10

Answer 1

Đặt A=1*2+2*3+3*4+........+9*10

3A=1*2*3+2*3*(4-1)+3*4*(5-2)+........+9*10*(11-8)

3A=1*2*3+2*3*4-1*2*3+3*4*5-2*3*4+........+9*10*11-8*9*10

3A=9*10*11

A=9*10*11:3

A=990:3

A=330

Answer 2

1*2 + 2*3 + 3*4 + 4*5 + ... + 9*10

= 1/3 . ( 1.2.3 + 2.3.3 + 3.4.3 + 4.5.3 + ... + 9.10.3)

= 1/3 . [ 1.2.3 + 2.3.(4-1) + 3.4.(5-2) + 4.5.(6-3) + ... + 9.10.(11-8)]

= 1/3 . ( 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + 4.5.6 - 3.4.5 + ... + 9.10.11 - 8.9.10)

= 1/3 . 9.10.11

= 3.10.11 = 330

Answer 3

Đặt A=1*2+2*3+3*4+........+9*10

3A=1*2*3+2*3*(4-1)+3*4*(5-2)+........+9*10*(11-8)

3A=1*2*3+2*3*4-1*2*3+3*4*5-2*3*4+........+9*10*11-8*9*10

3A=9*10*11

A=9*10*11:3

A=990:3

A=330

Answer 4

Đặt A = 1.2 + 2.3 + 3.4 + ... + 9.10

Ta có : 3 = 3 - 0 = 4 - 1 = 5 - 2 = .... = 11 - 8

=> 3A = 1.2.(3 - 0) + 2.3.(4 - 1)+ 3.4.(5 - 2) + ... + 9.10.(11 - 8 )

Aps đụng t/c : a.b.(c - e) = a.b.c - a.b.e

=> 3A = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 9.10.11 - 8.9.10

          = ( 1.2.3 - 1.2.3 ) + ( 2.3.4 - 2.3.4 ) + .... + ( 8.9.10 - 8.9.10 ) + 9.10.11

          = 9.10.11

\(\Rightarrow A=\frac{9.10.11}{3}=330\)