Question

1+3+5+…+2019=p la puterea a 2 a

Answer 1

Răspuns:

1 + 3 + 5 + 7 + ..... + 2019=(2019-1 ):2+1 =2018:2+1=1009+1=1010 termeni are suma

formula sumei lui Gauss

= 1010·( 1+2019 ):2 =1010·2020:2=1010·1010=1010 ²- patrat perfect

Answer 2

1+3+5+...+2019=
1+ 1•2 +1 + 2•2+1+...+2•1009 +1 =
1•1010 +2(1+2+3+...+1009)= (1 se repeta de 1010 ori și am dat factor comun pe 2)
1010 + 2• (1+1009)•1009 /2
1010 +1010•1009
1010(1+1009)
1010^2 => p=1010