Question

Demonstreaza ca numarul a este patrat perfect,unde a=1+2+3+...+100+51x101

Answer 1

$a=1+2+3+...+100+51*101= \\ ~~ = \frac{100*101}{2}+51*101= \\ ~~=50*101+51*101= \\ ~~=101(50+51)= \\ ~~=101*101= \\ ~~=101^2 ~-patrat~perfect.$

Answer 2

1+2+3.....100+51x101
100x(100+1):2+51x101
100x101:2+51x101
50x101+51x101=
101x(51+51)=
101x101=101²
101² este patrat perfect