Question

Aratati ca suma patratelor primelor 5 nr naturale nenule este divizibila cu 5

Answer 1

1²+2²+3²+4²+5²=1+4+9+16+25=55 -> 5|55
sau
U(1²)=1
U(2²)=4
U(3²)=9
U(4²)=6
U(5²)=5
=> 1+4+9+6+5=25 => 5|25

Answer 2

$\boxed{1^2+2^2+3^2+...+n^2=\dfrac{n(n+1)(2n+1)}{6}} \rightarrow formula.\\ \\ 1^2+2^3+3^2+4^2+5^2 = \dfrac{5(5+1)(2\cdot 5+1)}{6} =5\cdot \dfrac{6\cdot 11}{6} = 5\cdot 11 \vdots 5$