Question

Va rog ajutor.Cum arat ca numarul ,,9 ori (5+10+15+...+200) : 41'' este patrat perfect

Answer 1

   
[tex]\displaystyle\\ 9 \times (5+10+15+\cdot +200) : 41'' = \\\\ =9 \times 5 \times (1+2+3+\cdot +40):41 =\\\\ =9 \times 5 \times \frac{40\times 41}{2}:41 = \\\\ = 9 \times 5 \times 20 \times 41 : 41 = \\\\ = \frac{9 \times 5 \times 20 \times 41}{41} = \boxed{900 = 30^2 = pp}[/tex]