Question

1.Aratati ca numarul 9×(5+10+15+.....+200):41 este patrat perfect.

Answer 1

gauss in paranteza

5+10+15+...+200
5(1+2+....+40)=
5*40*41/2
 simplificam 40 cu 2=
5*20*41

introducem in ecuatie
9*5*20*41:41=
9*5*20=
900=> patrat perfect

Answer 2

=9 · 5 · ( 1+2+3+ .... + 40 ) :41 =
= 9· 5· ( 1 +40 ) · 40 /2    :41 = 
= 9· 5 · 41 · 20 :41 = 
= 9· 5 · 20 · 41:41 = 
 = 9 · 5· 20 ·1 = 900 = 30²