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

Răspuns :

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