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=(n+1)/(2(n+1)+1) - n/(2n+1)=
=(n+1)/(2n+3) - n/(2n+1)=
=[(n+1)(2n+1)-n(2n+3)]/[(2n+3)(2n+1)]=
=(2n^2+n+2n+1-2n^2-3n)/[(2n+3)(2n+1)]=
=1/[(2n+3)(2n+1)]
licznik jest dodatni
mianownik dla n€N jest dodatni
więc:
ciąg an jest rosnący