Question

1.2+2.3+3.4+.....+100.101

Answer 1

Ta có: 
A-B =1.2+2.3+3.4+...+100.101- 
(1^2+2^2+3^2+4^2+...+100^2) 
= 1.2+2.3+3.4+...+100.101- 

Answer 2

Đặt B = 1.2+2.3 +.......+99.100+100.101

3B= 1.2.3+2.3.4+3.4.3 +......+ 99.100.3 + 100.101.3

3B= 1.2. (3 - 0) + 2.3.(4 - 1) +3.4. (5 - 2)....... . 99.100. (101 - 98) . 100.101.(102 - 99)

3B = (1.2.3 + 2.3.4 + 3.4.5 +...... + 99.100.101 + 100.101.102) - (0.1.2 + 1.2.3 + 2.3.4 +.......+ 98.99.100.99.100.101)

3B = 100.101.102 - 0.1.2

3B = 1030200 - 0

3B= 1030200

B =  1030200 : 3

B =  343400

Answer 3

đặt A = 1.2+2.3+3.4+.....+100.101

=> 3A = 1.2.3+2.3.3+.......+100.101.3

=> 3A = 1.2.3+2.3.(4-1)+......+100.101.(102-99)

=> 3A = 1.2.3 + 2.3.4-1.2.3 + ........+ 100.101.102 - 99.100.101

=> 3A = 100.101.102

=> A = 100.101.102 : 3

=> A = 343400