Question

Cat e 1+3+5+...+997 plz rapid!!!!URGENT!!!!VA Rog!!!

Answer 1

1 + 3 + 5 + .... + 997 = 249 001

→ stabilesc cati termeni are suma cu ratia = 2 ( 3 - 1 = 2;   5 - 3 = 2;   ..... )

( 997 - 1 ) : 2 + 1 = 996 : 2 + 1 = 498 + 1 = 499 termeni are suma

→ aplic formula sumei lui Gauss

= 499 × ( 1 + 997 ) : 2 =

= 499 × 998 : 2 =

= 499 × 499 =

= 249 001

Answer 2

1 + 3 + 5 +...+ 997 =

2 × 1 - 1 + 2 × 2 - 1 + 2 × 3 - 1 +...+ 2 × 499 - 1 =

2 × (1 + 2 + 3 + .. + 499) - (1 + 1 + 1 +...+ 1 de 499 ori) =

2 × (499 × 500 : 2) - 1 × 499 =

499 × 500 - 499 =

499 × (500 - 1) =

499 × 499 =

499^2
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