Question

1+3+5+...+21=?

11+13+15+...+1081=?

Answer 1

1 + 3 + 5 + ......+ 21 = 121

→ aflu cati termeni are suma: ( 21 - 1 ) : 2 + 1 = 20 : 2 + 1 = 10 + 1 = 11 termeni, ratia = 2 ( 3 - 1 = 2; 5 - 3 = 2 ....)

→ suma primelor 11 numere naturale impare

→ aplic formula sumei lui Gauss

= 11 × ( 1 + 21 ) / 2 = 11 × 22 / 2 = 11 × 11 = 121

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11 + 13 + 15 + ......+ 1 081 =

( 1 081 - 11 ) : 2 + 1 = 1 070 : 2 + 1 = 536 → termeni are suma

= 536 × ( 11 + 1 081 ) / 2 = 268 × 1 092 =

= 292 656