Question

[Ác Quỷ Bóng Đêm]

Tính : A = 1.2 + 2.3 + 3.4 + ..... + 98.99 + 99.100

Answer 1

[Nguyễn Hưng Phát]

3A=1.2.3+2.3.(4-1)+.............+98.99.(100-97)+99.100.(101-98)

3A=1.2.3+2.3.4-1.2.3+...........+98.99.100-97.98.99+99.100.101-98.99.100

3A=99.100.101

A=99.100.101:3

A=333300

Answer 2

[Đinh Đức Hùng]

Ta có : 3A = 1.2.3 + 2.3.3 + 3.4.3 + .... + 98.99.3 + 99.100.3

=> 3A = 1.2.( 3 - 0 ) + 2.3.( 4 - 1 ) + 3.4.( 5 - 2 ) + ..... + 98.99.( 100 - 97 ) + 99.100.( 101 - 98 )

=> 3A = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ..... + 98.99.100 - 97.98.99 + 99.100.101 - 98.99.100

=> 3A = ( 1.2.3 + 2.3.4 + 3.4.5 + ..... + 98.99.100 + 99.100.101 ) - ( 0.1.2 + 1.2.3 + 2.3.4 + ..... + 98.99.100 )

=> 3A = 99.100.101 - 0.1.2

=> 3A = 99.100.101

=> A = 33.100.101

=> A = 333300