Question

1x2+2x3+3x4+...+98x99+99x100=?

giải đầy đủ giùm mk nha.

ai nhanh và đúng nhất mk tick cho

Answer 1

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

**** nha ^^

Answer 2

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

Answer 3

A = 1x2 + 2x3 + 3x4 + ... + 98x99 + 99x100

A x 3 = 1x2x3 + 2x3x3 + 3x4x4 + ... + 99x100x3

A x 3 = 1x2x3 + 2x3 x ( 4 - 1 ) + 3x4( 5 - 2 ) + 4x5x (6 - 3 ) + .... + 99x100( 101 - 98 )

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

A x 3 = 99 x 100 x 101

A = 99x 100 x 101 : 3 

A = 333300

Answer 4

Đặt A = 1x2 + 2x3 + 3x4 + ... + 98x99 + 99x100

3A = 1x2x(3-0) + 2x3x(4-1) + 3x4x(5-2) + ... + 98x99x(100-97) + 99x100x(101-98)

3A = 1x2x3 - 0x1x2 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + ... + 98x99x100 - 97x98x99 + 99x100x101 - 98x99x100

3A = (1x2x3 + 2x3x4 + 3x4x5 + ... + 98x99x100 + 99x100x101) - (0x1x2 + 1x2x3 + 2x3x4 + ... + 97x98x99 + 98x99x100)

3A = 99x100x101 - 0x1x2

3A = 99x100x101

A = 33x100x101

A = 333 300

Ủng hộ mk nha ^-^
 

Answer 5

Tại sao Ax3 nhỉ ?

Answer 6

3x4?(5-2)