Question

Tính:

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

Answer 1

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

=>3S=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+...+99.100.101-98.100.101

=99.100.101=999900

=>S=333300

vậy S=333300

Answer 2

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

3.S = 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 - 98.100.101

      = 99.100.101 = 999900

3.S = 999900

S = 333300

Answer 3

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

=> 3S = 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 - 98.100.101

= 99.100.101 = 999900 

=> S = 3S : 3 = 999900 : 3 =33300

Vậy S =333300