Question

Demonstreaza ca numarul a este divizibil cu 5 ,undr :a=2+4+6+....+78

Answer 1

a=2+4+6+....+78 /5
a=2(1+2+3+.....+39)×$\frac{39}{2}$
a=(1+39)×39
a=40×39
a=1560 /5 (adevarat)

Answer 2

a = 2 + 4+ 6 + ... + 78 

Impartim relatia la 2:

a : 2 = 1 + 2 + ... + 39

Aplicand suma Gauss:

a : 2 = 39 · 40 / 2
a = 39 · 40
a = 1560  ⇒  5 | a