Question

URGENT

aratati ca nnumarul 9*(5+10+15+...+200):41 este patrat perfect

Answer 1

in primul rand suma (5 + 10 + 15+...+200) = 5(1+2+3...+40) = 5 * 40*41 : 2  = 5* 20 * 41
Deci rezulta ca numarul nostru este 9 * 20* 5 * 41 : 41 = 900
Iar 900 =  => patrat perfect

Answer 2

modul 1:
9*(5+10+15+.........+200):41=
mai intai vom calcula 5+10+15+........+200
5+10+15+........+200=(200+5)*(numarul de termeni):2
numarul de termeni=(200-5):5+1=195:5+1=39+1=40
(200+5)*40:2=205*20=4100
9*4100:41=36900:41=900=30*30
modul 2:
9*(5+10+15+.........+200):41=
mai intai vom calcula 5+10+15+........+200
5+10+15+.........+200=5*(1+2+3........+40)=5*[40*(40+1):2]=5*(20*41)=5*820=4100
9*4100:41=36900:41=900=30*30