Question

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

Answer 1

Suma=(5+10+15+...+200)=5(1+2+3+...40)=5*40*41:2=5*20*41
Rezulta ca numarul nostru este 9*20*5* 41:41=900
900=30 la a 2=patrat perfect

Answer 2

9*5(1+2+3+...+40):41=

utilizam formula :$1+2+3+...+n= \frac{n(n+1)}{2}$

$9*5* \frac{40*41}{2}:41 =45*20*41:41=45*20=900= 30^{2}$