Question

calculati 3+7+11+...+399-1-5-9-...-397=?

Answer 1

3 + 7 + 11 + ........ + 399 - 1 - 5 - 9 - .........- 397 = 200

= (3 + 7 + 11 + ......+ 399 ) - ( 1 + 5 + 9 + .......+ 397 ) =

→7 - 3 = 4 ( r) ; ( 399 - 3) : 4 + 1 = 396 : 4 + 1 = 99 + 1 = 100 termeni are prima suma

→5 - 1 = 4 ( r) ; ( 397 - 1 ) : 4 + 1 = 100 termeni are si a doua suma

→ aplic formula sumei lui Gauss

= [ 100 × ( 3 + 399 ) / 2] - [ 100 × ( 1 + 397 ) / 2] =

= ( 50 × 402 ) - ( 50 × 398 ) =

= 20 100 - 19 900 =

= 200