Question

10 )Aratai ca nr N=(1+2+3+....+99)•2+100 este patrat perfect

Answer 1

Ai suma Gauss: 1 + 2 + 3 + ... + 99 = ( 99 * 100 ) / 2 ;
Atunci : (1+2+3+....+99)•2 = 99 * 100;La final, 99 * 100 + 100 = ( 99 + 1 )*100 = $100^{2}$, care e patrat perfect.
Bafta!