Question

aratati ca urmatoarele numere sunt patrate perfecte: 1+3+5+...55=

Answer 1

1 + 3 + 5 + ...... + 55 = 784

→ stabilesc cati termeni are suma cu ratia = 2 ( 3 -1 = 2;   5 - 3 = 2;.... )

( 55 - 1 ) : 2 + 1 = 54 : 2 + 1 = 27 + 1 = 28 termeni are suma

→ aplic formula sumei lui Gauss

= 28 × ( 1 + 55 ) : 2 =

= 28 × 56 : 2 =

= 28 × 28 =

= 28² → patrat perfect