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Dati factor comun: 5+10+15+...+90=?

Răspuns :

5(1+2+3+...+18)  facem gauss in paranteza

18*19/2 = 9*19 = 171

Deci 5*171 = 855

5 + 10 + 15 + ...... + 90 = 855

= 5 × ( 1 + 2 + 3 + ....... + 18 ) =

= 5 × 18 × ( 1 + 18 ) / 2  =

= 90 × 19 / 2 =

= 1 710 / 2 =

= 855