Question

aratati ca radical din 1+3+5.........+19 apartin lui Q

Answer 1

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

se poate scrie astfel:
1+2*0 + 1+2*1 +1+2*2+...+1+2*9 =
1*10+2*(1+2+...+9)=
10+2*9*10/2=
10+90=100
√100=10 ∈ Q   q.e.d

Answer 2

M=1+3+5+...+19
M=19+...+5+3+1
------------------------
2M=20+...+20+20
Numar termeni: (19-1)/2+1=18/2+1=9+1=10
M=10x20/2
M=10x10
M=10²
$\sqrt{1+3+5+...+19}= \sqrt{10^{2} }=10 =\ \textgreater \ \sqrt{1+3+5+...+19}∈Q$



Sper ca te-am ajutat ! :)