Aplici Lema lui Stolz
an=ln(1+e^n) bn=n n→+∞
Lim an/bn=lim[(an+1)-an]/[bn=1-bn]=
lim[ln(1+e^(n+1)-ln(1+e^n]/(n+1-n)=
lim[ ln(1+e^(n+1)-ln(1+e^n)=
limln(1+e*e^n)/(1+e^n)=dai factor comun fortat la numarator si numitor pre e^n
limlne^n*(1/e^n+e)/e^n(1/e^n+1)=limln(1/e^n+e)/(1/e^n+1)=logaritmul comuta cu limita
lnlim(1/e^n+e)/(1/e^n+1)=lne=1 pt ca 1/e^n→0
