Question

Aratati ca numarul a este patrast perfect

A)a egal (1+2+3+....+99)*2+100
b) a egal 1+2+3+.......+50-25*50
c)a egal 3+6+9+......+75-75

Answer 1

A)a egal (1+2+3+....+99)*2+100
a=100·99/2·2+100=100·99+100=100(99+1)=100²
b) a egal 1+2+3+.......+50-25*50
a=51·50/2-25·50=51·25-25·50=25(51-50)=25=5²
c)a egal 3+6+9+......+75-75
a=3+6+9+...+72=3(1+2+3+...+24)=3·25·24/2=25·36=(5·6)²=30²