Question

Arătați ca nr a e nr perfect
A= (2+4+6+...+100)-50

Answer 1

A=2*(1+2+3+...+50)-50 = 2*(50*51:2) - 50 =
   = 50*51 - 50 = 50*(51-1) = 50² =p.p. (=2500) .

Answer 2

A= (2+4+6+...+100) - 50 => A = 2(1+2+3+..+50) - 50 => 
=>$A=2* \frac{50*51}{2}-50 = 50*51 - 50 = 50(51-1) = 50*50$

Deci A = 2500 este numar perfect.