Question

[Chu Dieu Ha]

1*2+2*3+3*4+..........+99*100

Answer 1

[Han Sara ft Tùng Maru]

1 x 2 + 2 x 3 + 3 x 4 + ... + 99 x 100

Đặt A = 1 x 2 + 2 x 3 + 3 x 4 + ... + 99 x 100

=> 3A = 1 x 2 x 3 + 2 x 3 x 3 + 3 x  4 x 3 + ... + 99 x 100 x 3

           = 1 x 2 x 3 + 2 x 3 x ( 4 - 1 ) + 3 x 4 x ( 5 - 2 ) + ... + 99 x 100 x ( 101 - 98 )

           = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + 3 x 4 x 5 - 2 x 3 x 4 + ... + 99 x 100 x 101 - 98 x 99 x 100

           = 99 x 100 x 101

           = 999900 => 999900 : 3 = 333300

Học tốt #

Answer 2

[OneHit_One KIll]

Đặt S = 1.2 + 2.3 + 3.4 + ... + 99.100 

3S = 1.2.3 + 2.3.3 + 3.4.3 + ... + 99.100.3

3S = 1.2.3 + 2.3.(4-1) + 3.4.(5-2) + ... + 99.100.(101-98)

3S = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 99.100.101 - 98.99.100 

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

3S = 99.100.101 

S = \(\frac{99.100.101}{2}\)= 333300 

Vậy S = 333300