Question

Tính. 

A = 1.2+2.3+3.4+....+99.100

Answer 1

Gọi biểu thức là A, ta có: 
A = 1.2+2.3+3.4+......+99.100 
Gấp A lên 3 lần ta có: 
A . 3 = 1.2.3 + 2.3.3 + 3.4.3 + … + 99.100.3 
A . 3 = 1.2.3 + 2.3.(4 - 1) + 3.4.( 5 - 2) + … + 99.100. (101 - 98) 
A . 3 = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + … + 99.100.101 - 98.99.100 
A . 3 = 99.100.101 
A = 99.100.101 : 3 
A = 33.100.101 
A = 333 300

Answer 2

Ta có : \(\text{A = 1.2 + 2.3 + 3.4 + ....... + 99.100}\)

=> \(\text{3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ...... + 99.100.101}\)

=> \(\text{3A = 99.100.101}\)

=> \(A=\frac{99.100.101}{3}\)

=> \(\text{A = 333300}\)

Answer 3

Đặt A = 1.2+2.3+3.4+....+99.100

3A = 1.2.3+2.3.4+3.4.5+.....+99.100.3

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

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

3A = 99.100.101 - 0.1.2

3A = 999900 - 0

3A = 999900

  A = 999900 :3

  A = 333300