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