Question

A) 1+2+3+ ........... + 135

B) 2+4+6+...........+136

C) 1+3+5+............+137

D) 3+6+9+12+.........+123


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Answer 1

A) 1+2+3+...+135=

=135×(135+1):2=

=135×136:2=

=135×68=

=9180

B) 2+4+6+...+136=

=2×(1+2+3+...+68)=

=2×68×(68+1):2=

=2×34×69=

=68×69=

=4692

C) 1+3+5+...+137=

=1+2+3+4+5+...+136+137-(2+4+6+...+136)=

=137×(137+1):2-2×(1+2+3+...+68)=

=137×138:2-2×68×(68+1):2=

=137×69-68×69=

=9453-4692=

=4761

D) 3+6+9+12+...+123=

=3×(1+2+3+...+41)=

=3×41×(41+1):2=

=3×41×42:2=

=3×41×21=

=123×21=

=2583