Question

1+3+5+......+1007 sa fie pătrat perfect

Answer 1

1 + 3 + 5 + 7 + ......+ 1 007 =

→ aflam cati termeni are suma; ratia = 2

( 1 007 - 1 ) : 2 + 1 = 1 006 : 2 + 1 = 503 + 1 = 504 termeni are suma

→ aplic formula sumei lui Gauss

= 504 × ( 1 + 1 007 ) / 2 = 504 × 1 008 / 2 = 504 × 504 = 504²→ patrat perfect