Ai suma Gauss 1+2+3+......k = k(k+1)/2 = ( k^2 + k )/2, oricare ar fi k nr. natural nenul;
Atunci 1 = ( 1^2 + 1 )/2;
1+2 = ( 2^2 + 2 )/2
1+2+3 = ( 3^2 + 3 )/2
........................................................
1+2+3+.......+n = ( n^2 + n )/2
Aduni una sub alta cele n relatii matematice
=> 1+(1+2) +(1+2+3) +1+2+3+4)+........+.(1+2+3+......n) = [(1^2 + 2^2 +3^2+....+n^2) + (1+2+3+...+n)]/2;
Folosesti formulele:
a) 1^2 + 2^2 +3^2+....+n^2 = n(n+1)(2n+1)/6 si,
b) 1+2+3+......+n = n(n+1)/2;
Si gata!
Bafta!
