a)aplici Lema lui Stolz
notezi xn numaratorul yn numitorul yn→∞
lim(xn+1-xn)/(yn+1-yn)=lim xn/yn
lim an=lim (ln(n+1)-ln]/(n+1-n)=limln(n+1)/1=ln1=0
b)aplicand formula de mai sus se ajunge la
lim(ln2+ln3+....+ln(n+1)-ln2-ln3-....lnn)/(n+2-n-1)=lim(ln(n+1)-ln)n/]/1=lim ln(n+1)/n=0
c)Inmultesti paranteza cu 1/n
scze revin
consideri paranteza la nu marator si 1/n la numitor si aplici lema lui stolz
lim(1+1/2+....+1/n+1/(n+1)-1-1/2-...-1/n]/(n+1-n=lim(1/(n+1)/1=0
