Question

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

Answer 1

1+2+.....+ 100 = ( 1+ 100) · 100 :2 = 101 · 50 = 5050 
101 · 50 + 101 ·51 = 101 ( 50 + 51 ) = 101· 101 = 101² patrat perfect 

Answer 2

$1+2+3+...+100+51*101= \\ \frac{100*101}{2} +51*101$
(Am folosit Suma Gauss)
$50*101+51*101= \\ 101(50+51)= \\ 101*101= 101^{2}$