Question

Chứng minh rằng 1.2+2.3+3.4+...+98.99=98.99.100:3

Answer 1

 Đặt s = 1.2+2.3+...+98.99

Suy ra 3s=1.2.(3-0)+2.3.(4-1)+...+98.99.(100-97)

=1.2.3-0.1.2+2.3.4-1.2.3+...+98.99.100-97.98.99

=98.99.100

Nên s=98.99.100:3

Answer 2

Đặt A =1.2 + 2.3 + 3.4 + ... + 98.99 

3A = 1.2.3 + 2.3.3 + 3.4.3 + ... + 98.99.3 

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

3A = 1.2.3 + 2.3.4 + 3.4.5 + ... + 98.99.100 

3A = 98.99.100 

=> A = 98.99.100 : 3 (đcmp)