Question

12+18+24+30+.....+408=suma lui gauss

Answer 1

Răspuns:

14 070

Explicație pas cu pas:

12+18+24+30+...+408 =

1×6+6 + 2×6+6 + 3×6+6 + 4×6+6+...+ 67×6+6 =

6×(1+2+3+4+..+ 67) + 6 × 67 =

6 × 67 × (67+1) : 2 + 6 × 67 =

3 × 67 × 68 + 6 × 67 =

67 × ( 3 × 68 + 6) =

67 × (204+6) =

67 × 210 =

14 070

___________

Answer 2

12+18+24+30+...+408 =

= 6·(2+3+4+5+...+68) =

= 6·(-1+1+2+3+4+5+...+68) =

= -6 + 6·(1+2+3+4+5+...+68) =

= -6 + 6·[68·(68+1)]/2 =

= -6 + 3·68·69 =

= -6 + 14076 =

= 14070