Question

Ajutatima :
5+6+7...........+81=
1+2+3...........+512=
317+318+319+..........+400=

Answer 1

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