Question

Demonstreaza ca numarul a este patrat perfect,unde a=1+2+3...+100+51×101

Answer 1

1+2+3+...+100=(100+1)*100/2=101*50
101x50+101x51=101(50+51)=101x101=101²

Answer 2

$1+2+3+....+100\to \frac{100}{2} *(100+1)\to\boxed{101*50} \\ \\ 101*50+101*51\to101*(50+51)\to101*101\to \boxed{101^{2} } \\ \\ \\ Si.daca.esti.curios/curioasa: 101^{2}\to10201.$