Question

Arata ca nr n=1+2+....+20+75:5 este patrat perfect.Va rog ajutati.ma urgent.

Answer 1

n=1+2+...+20+75÷5
n=1+2+...+20+15
n=20×21÷2+15
n=210+15
n=225 =>
$\sqrt{225 } = 15$
=> n este patrat perfect

Answer 2

n = 1 + 2 + .....+ 20 + 75 : 5

→ calculez mai intai suma celor 20 de termeni; aplicand formula sumei lui Gauss  

1 + 2 + 3 + ..... + 20 = 20 x ( 1 + 20 ) / 2 = 10 x 21 = 210

n = 210 + 15

n = 225

n = 15 ² → patrat perfect

√225 = 15