Question

tính tổng D=1.2+2.3+3.4+..........+99.100

Answer 1

D=1.2+2.3+3.4+...+99.100

=>3D=1.2.3+2.3.3+3.4.3+...+99.100.3

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

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

=99.100.101=999900

=>D=333300

Answer 2

Đặt S= 1.2 + 2.3 + 3.4 + ...+ 99.100
 3S = 1.2.3+2.3.3+3.4.3+...+98.99.3+99.100.3
3S= 1.2.3+2.3(4-1)+3.4(5-2)+...+98.99(100-97)+99.100(101-98)
3S= 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...-97.98.99+99.100.101-98.99.100
3S = 99.100.101  3S = 3.33.100.101 
 S=33.100.101= 333300

Answer 3

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

⇒ 3A = 1.2.3 + 2.3.3 + 3.4.3 + .... + 99.100.3

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

⇒ 3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ..... + 99.100.101 - 98.99.100

⇒ 3A = ( 1.2.3 - 1.2.3 ) + ( 2.3.4 - 2.3.4 ) + .... + ( 98.99.100 - 98.99.100 ) + 99.100.101

⇒ 3A = 99.100.101

⇒ A = ( 99.100.101 ) : 3 = 333300