Question

1.2+2.3+3.4+4.5+...+99.100

Answer 1

1.2+2.3+3.4+4.5+...+99.100

=1.2.3+2.3.3+3.4.3+4.5.3+...+99.100.3

=1.2.3+2.3.(4-1)+3.4.(5-2)+4.5.(6-3)+...+99.100.(101-98)

=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+4.5.6-3.4.5+...+99.100.101-98.99.100

=1.2.3-1.2.3+2.3.4-2.3.4+3.4.5-3.4.5+4.5.6-4.5.6+...+99.100.101

=99.100.101=999900

=999900:3=333300