Question

Aratati ca 1+3+5+...+999 = 500^2. Putin ajutor, am incercat cu progresie, dar nu imi iese. Multumesc!​

Answer 1

1 = [(1+1)/2]²

1+3 = [(3+1)/2]²

1+3+5 = [(5+1)/2]² = 3²

1+3+5+7 = [(7+1)/2]² = 4²

1+3+5+7+9 = [(9+1)/2]² = 5²

⋮ (analog)

1+3+5+...+n = [(n+1)/2]²   -   (Formulă)

⇒  1+3+5+...+999 = [(999+1)/2]² = (1000/2)² = 500²