Question

Calculati:1+3+5+...+19

Answer 1

1+3+5+...2n-1=n*n
19=2×10-1 n=10
suma este 10×10


sau cuplezi
(1+19)+(2+18)+(3+17)+(4+16)+...(9+11)=5×20=100

Succes !

Answer 2

1 + 3 + 5 + ....... + 19 = 100

= ( 1 + 19 ) + ( 3 + 17 ) + ( 5 + 15 ) + ( 7 + 13 ) + ( 9 + 11 ) = → asociativitate

= 20 + 20 + 20 + 20 + 20 =

= 100

________________________

sau:

→ stabilesc cati termeni are suma cu ratia = 2

( 19 - 1 ) : 2 + 1 = 9 + 1 = 10 termeni

→ aplic formula sumei lui Gauss

= 10 × ( 1 + 19 ) : 2 =

= 10 × 20 : 2 =

= 200 : 2 =

= 100