5 + 6 + 7+ .......... + 81 = 3 311
→ stabilesc cati termeni are suma cu ratia 1 ( 6 - 5 = 1 ; 7 - 6 = 1 ... )
81 - 5 + 1 = 77 termeni are suma
→ aplic formula sumei lui Gauss
= 77 × ( 5 + 81 ) / 2 =
= 77 × 86 / 2 =
= 77 × 43 =
= 3 311
_________________________
1 + 2 + 3 + ........... + 512 = 131 328
= 512 × ( 1 + 512 ) / 2 =
= 256 × 513 =
= 131 328
_______________________
317 + 318 + 319 + .......... + 400 = 30 114
( 400 - 317 ) + 1 = 84 termeni are suma cu ratia = 1 ( 318 - 317 = 1 )
= 84 × ( 317 + 400 ) / 2 =
= 42 × 717 =
= 30 114
