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Stabiliti ca n=36•1+36•2+36•3+..........+36•999 este patrat perfect?
20 pnct


Răspuns :

ai 36*(1+2+...+999) = 36*(1+999)*999/2 = scoti in factori primi si observi ca nu e pp... 
pt suma aplici formula (primul termen+ ultimul termen )*nr de termeni/2
36×1+36×2+36×3+.....+36×999=
36×(1+2+3+.....+999)=
36×[999×(999+1):2]
36×(999×1000:2)=
36×(999000:2)=
36×499500=
17982000