Question

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

Answer 1

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

Answer 2

$a=1+2+3.....+100+51*101= \frac{101*100}{2}+51*101$ $=101*50+51*101 = 101(50+51) = 101*101 = 101^2$ ⇒ a = p.p.