Question

(3+6+9+...+369)-(2+4+6+...+246)

Answer 1

(3+6+9+...+369)-(2+4+6+...+246)=
=3(1+2+..+123)-2(1+2+..+123)
=3·123·124:2-2·123·124:2
=22878-15252
=7626

Answer 2

S=(3+6+9+...+369)-(2+4+6+...+246)

S1=(3+6+9+...+369)= 3 × (1+2+3+.....+123)=3×[123×(123+1)]:2 = 22878

S2= (2+4+6+...+246) = 2×(1+2+3+.....+123)=2×[123×(123+1)]:2=15252

S = S1 - S2 = 22878 - 15252 = 7626

sau

S=S1-S2=3 × (1+2+3+.....+123)=3×[123×(123+1)]:2 - 2 × (1+2+3+.....+123)=3×[123×(123+1)]:2 =([123×(123+1)]:2)(3-2)=([123×(123+1)]:2)=7626