Question

demonstreaza ca numarul a este patrat unde a=1+2+3+.....+100+51 ori 101

Answer 1

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

Answer 2

a=1+2+3+....+100+51x101=
a=100x(100+1):2+51x101=
a=100x101:2+51x101=
a=10100:2+51x101=
a=5050+5151=
a=10201
a=101²
101² este patrat perfect