Question

tinh nhanh A=1*2+2*3+3*4+4*5+...+99*100

 

Answer 1

A = 1*2+2*3+3*4+4*5+...+99*100 

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

=> 3A = 99.100.101

=> A = 99.100.101 / 3 = 333300

Answer 2

S = 1 x 2 + 2 x 3 + ... + 99 x 100

3S = 1 x 2 x 3 + 2 x 3 x (4 - 1) + ..... + 99 x 100 x (101 - 98)

3S = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + .... + 99 x 100 x 101 - 98 x 99 x 100

3S = 99 x 100 x 101 = 999900

S = 999900 : 3 = 333300

Answer 3

A = 333300

Answer 4

Gọi biểu thức trên là A, ta có :

A = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100

A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3

A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)

A x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.

A x 3 = 99x100x101

A = 99x100x101 : 3

A = 333300

k mk nha!!!!