c) S = 101 + 102 + 103 + ...... + 998 + 999 + 1 000
S = 1 000 + 999 + 998 + ......+103 + 102 + 101
____________________________________
2 × S = ( 101 + 1 000 ) + ( 102 + 999 ) + ....... + ( 999 + 102 ) + ( 1 000 + 101 )
2 × S = 1 101 + 1 101 + 1 101 + ......... + 1 101 + 1 101
____________________________________
→ stabilesc cati termeni are suma: 1 000 - 101 + 1 = 899 + 1 = 900 termeni are suma
→ sunt 900 de sume
_______________________________
2 × S = 900 × 1 101
S = 990 900 : 2
S = 495 450
__________________________
sau aplic formula sumei lui Gauss:
S = 900 × ( 101 + 1 000 ) : 2
S = 450 × 1 101
S = 495 450
