Question

demonstreaza ca numarul a 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

 $a=\underbrace{1+2+3+...+100}_{=\frac{100\cdot101}{2}=50\cdot101}+51\cdot101=101(50+51)=101^2$