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
