Question

Calculați si arătați ca este pătratul unui număr natural.
a.)x=1+2+3+...+224+16*450
b.)x=2+4+6+...+100-25*2
c.)x=1+2+3+...+120+2*242

Answer 1

a.)x=1+2+3+...+224+16*450
x=224*225:2+16*450
x=25200+7200
x=32400 
            2
x=180
b.)x=2+4+6+...+100-25*2
x=2(1+2+3+...+50)-25*2
x=2(50*51:2)-25*2
x=2x1275-50
x=2550-50
x=2500
         2
x=50

c.)x=1+2+3+...+120+2*242
x=1+2+3+...+120+2*242
x=120*121:2+2*242
x=7260+484
x=7744
         2   
x=88

Answer 2

a.)x=1+2+3+...+224+16*450= 224*225/2+ 16*450=112*225+16*450=
=25200+7200=32400=180²

b.)x=2+4+6+...+100-25*2
x=2*(1+2+3+...50) -50
x=2*50*51/2- 50
x=2550-50
x=2500
x=50²

c.)x=1+2+3+...+120+2*242
x=120*121/2 + 484
x=7260 +484
x=7744
x=88²