( 2 + 4 + 6 + ...... + 20 ) - ( 1 + 2 + 3 + ....... + 19 ) =
= 2 × ( 1 + 2 + 3 + ...... + 10 ) - [ 19 × ( 1 + 19 ) : 2 ] =
= 2 × 10 × ( 1 + 10 ) : 2 - ( 19 × 20 : 2 ) =
= 10 × 11 - 19 × 10 =
= 10 × ( 11 - 19 ) =
= 10 × ( - 8 ) =
= - 80
_______________________________
Daca e diferenta dintre suma primelor 10 numere pare si 10 numere impare, atunci;
( 2 + 4 + 6 + ...... + 20 ) - ( 1 + 3 + 5 + ... + 19 ) =
= 2 × ( 1 + 2 + 3 + .... + 10 ) - ( 10 × 20 : 2 ) =
= 2 × 10 × 11 / 2 - 10 × 10 =
= 110 - 100 =
= 10
_________
1 + 3 + 5 + .... + 19 = 10 × ( 1 + 19 ) : 2 = 5 × 20 = 100
→ stabilesc cati termeni are suma cu ratia = 2
( 19 - 1 ) : 2 + 1 = 10 termeni are suma
→ aplic formula sumei lui Gauss
