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a=81+2*81+3*81+...+49*81

Răspuns :

[tex]A=81(1+2+3+...+49)= \\ \\ ~~~=81 \cdot \frac{49 \cdot 50}{2}= \\ \\ ~~~=81 \cdot 49 \cdot 25= \\ \\ ~~~=9^2 \cdot 7^2 \cdot 5^2= \\ \\ ~~~= \boxed{ (5 \cdot 7 \cdot 9)^2}-patrat~perfect[/tex]
A=81*(1+2+3+...+49)=81* [tex]\frac{49\cdot50}{2}[/tex]
A=81 * 49 * 25 = (5*7*9)² = 315² =99225;