Question

Pls, E1 punctul b). E cu lema lui Stolz Caesaro, dar imi da rezultatul (+ infinit)
Unde am gresit?

Answer 1

n+1=bn>0∀n

(bn+1)/bn=(n+2)/(n+1)>1∀n=>(bn)->strict crescator

lim bn=+∞=>∃  lim[(an+1-an)/(bn+1-bn)]=lim[(ln2+ln3+...+ln(n+1)-ln2-ln3-...-lnn)/(n+2-n+1)=lim ln(n+1)=lim [ln(n+1)]*n/n=1*lim n=1*+∞=+∞