Question

1+2 +3.......+400 2+4+6...... +400

Answer 1

1+2 +3.......+400suma lui Gauss
S=]400*(1+400)]/2=(400*401)/2=80200

S2=2+4+6...... +400 =2(1+2+3+.......+200)
La paranteza la fel Suma lui Gauss
S2=2 * [200*(1+200)]/2=2 * (200*201)/2=40200

Answer 2

$\displaystyle a).1+2+3+...+400= \frac{400(400+1)}{2} = \frac{400 \times 401}{2} = \frac{160400}{2} =80200 \\ \\ b).2+4+6+...+400=2(1+2+3+...+200)=2 \times \frac{200(200+1)}{2} = \\ \\ =2 \times \frac{200 \times 201}{2} =\not 2 \times \frac{40200}{\not 2} =40200$