Question

Am nevoie de ajutor repede ​

Answer 1

Răspuns:

x=√(1/100)=1/10 ∈Q

Explicație pas cu pas:

1/1•2+1/2•3+...+1/24•25=

=1/1-1/2+1/2-1/3+....+1/24-1/25

=1/1-1/25

1/25•26+1/26•27+...+1/49•50=

=1/25-1/26+1/26-1/27+....+1/49-1/50

=1/25-1/50

1/94[1/1•2+1/2•3+...+1/24•25-(1/25•26+1/26•27+...+1/49•50)]=

=1/94[1/1-1/25-(1/25-1/50)]

=1/94(1/1-2/25+1/50)

=1/94[(50-4+1)/50]

=1/94•(47/50)

=1/2• 1/50

=1/100

x=√(1/100) = 1/10 ∈Q